34 + Interview Questions in Arithmetic Progressions in Mathematics

1.	How many terms of the AP 5,10,15,20….. must be added to get a sum of 330?(a) -11(b) -12(c) 12(d) 11The question was asked in final exam.My question is based upon Sum of N Terms of Arithmetic Progression topic in portion Arithmetic Progressions of Mathematics – Class 10
Answer» Right OPTION is (d) 11 Explanation: Here a = 5, d = 5 and Sn = 330 We KNOW that, Sn = \(\frac {n}{2}\) (2A + (n – 1)d) 330 = \(\frac {n}{2}\) (2(5) + (n – 1)5) 330 = \(\frac {n}{2}\) (10 + 5n – 5) 330 = \(\frac {n}{2}\) (5 + 5n) 330 = \(\frac {5n^2+5n}{2}\) 660 = 5n^2 + 5n n^2 + n – 132 = 0 n = -12, 11 Since, n cannot be negative Hence value of n is 11.

Discussion

2.	The sum of the first 12 terms of an AP is 15 and the sum of its first 15 terms is 12, then the sum of its first 27 terms will be __________(a) -24(b) 24(c) 27(d) -27The question was posed to me in quiz.Question is taken from Sum of N Terms of Arithmetic Progression in division Arithmetic Progressions of Mathematics – Class 10
Answer» Right option is (d) -27 Easy EXPLANATION: The sum of the FIRST 12 terms of an AP is 15 S12 = 15 \(\frac {n}{2}\) (2a + (n – 1)d) = 15 \(\frac {12}{2}\) (2a + (12 – 1)d) = 15 6(2a + 11d) = 15 12a + 66d = 15 4a + 22d = 5(1) The sum of its first 15 terms is 12 S15 = 12 \(\frac {n}{2}\) (2a + (n – 1)d) = 12 \(\frac {15}{2}\) (2a + (15 – 1)d) = 12 \(\frac {15}{2}\) (2a + 14d) = 12 15(a + 7d) = 12 15a + 105d = 12 5A + 35d = 4(2) On subtracting (2) from (1) 4a + 22d – (5a + 35d) = 5 – 4 -a – 13d = 1 a + 13d = -1(3) Now, S27 = \(\frac {n}{2}\) (2a + (n – 1)d) = \(\frac {27}{2}\) (2a + (27 – 1)d) = \(\frac {27}{2}\) (2a + 26d) = 27(a + 13d) = -27from (3).

Discussion

3.	If the 7^thterm of an AP is 20 and its 11^thterm is 40 then, what will be the common difference?(a) 3(b) 4(c) 5(d) 2The question was asked in an online quiz.The query is from Nth Term of Arithmetic Progression topic in division Arithmetic Progressions of Mathematics – Class 10
Answer» The correct answer is (c) 5 Explanation: Here 7^thterm = 20 11^thterm = 40 Let the FIRST term of the AP be a and common DIFFERENCE be d T7 = a + (n – 1)d = 20 T7 = a + (7 – 1)d = 20 T7 = a + 6d = 20(1) T11 = a + (n – 1)d = 40 T11 = a + (11 – 1)d = 40 T11 = a + 10D = 40(2) Subtracting (1) from (2) We get, a + 10d – (a + 6d) = 40 – 20 4d = 20 d = 5

Discussion

4.	If the p^th term of an AP is q and its q^th term is p, then what will be the value of its (p + q)^th term?(a) 1(b) p + q – 1(c) 0(d) 2(p + q – 1)The question was posed to me during an online exam.Origin of the question is Nth Term of Arithmetic Progression in chapter Arithmetic Progressions of Mathematics – Class 10
Answer» Right CHOICE is (c) 0 Easiest explanation: p^th TERM = q a + (p – 1)d = q a + pd – d = q(1) q^th term = p a + (q – 1)d = p a + qd – d = p(2) Subtracting (2) from (1) we get, a + qd – d – (a + pd – d) = p – q qd – pd = p – q d = -1 Substituting in equation 1, we get, a = p + q – 1 (p + q)^th term = a + (n – 1)d = p + q – 1 + (p + q – 1)(-1) = p + q – 1 – p – q + 1 = 0

Discussion

5.	If the n^thterm of the AP is 7n – 9, then the first term is ________(a) 1(b) 6(c) 3(d) 4The question was asked in quiz.This interesting question is from Nth Term of Arithmetic Progression topic in portion Arithmetic Progressions of Mathematics – Class 10
Answer» RIGHT CHOICE is (B) 6 To explain: n^th term of the AP is 7n – 9 Tn = 7n – 1 T1 = 7(1) – 1 = 6 The first term of AP is 6.

Discussion

6.	The sum of three numbers is 30 and their product 750. What are the three numbers?(a) -2, -6 and -10(b) 2, 6, and 10(c) 5, 10 and 15(d) -5, -10 and -15The question was posed to me in homework.I would like to ask this question from Arithmetic Progression Basics in portion Arithmetic Progressions of Mathematics – Class 10
Answer» Right ANSWER is (c) 5, 10 and 15 For EXPLANATION: Let the three NUMBERS in AP be (a + d), a, and (a – d). Sum of the five numbers is 30. ∴ (a + d) + a + (a – d) = 30 3a = 30 a = 10 Now, product of the numbers is 750. ∴ (a + d)a(a – d) = 750 a^3 – d^2 a = 750 Substituting a = 10, we get 10^3 – d^2 (10) = 750 1000 – d^2 (10) = 750 250 = 10d^2 d^2 = 25 d = 5, -5 The three numbers are 5, 10 and 15.

Discussion

7.	If the first term of an AP is a and its common difference is d then the nth term is given by Tn = a + (n – 1)d(a) True(b) FalseThis question was addressed to me in my homework.I want to ask this question from Arithmetic Progression Basics in chapter Arithmetic Progressions of Mathematics – Class 10
Answer» RIGHT option is (a) True Easiest explanation: In the given AP we have, FIRST term as a and COMMON difference as d. So, the given AP may be written as a, a + d, a + 2d, a + 3d, … In this AP, we have, First term = a = a + (1 – 1)d Second term = a = a + (2 – 1)d Third term = a = a + (3 – 1)d And so, on Hence, the n^th term of the AP will be a + (n – 1)d.

Discussion

8.	How many terms are there in the AP 9, 16, 23, 30……………282?(a) 50(b) 45(c) 40(d) 42I had been asked this question during a job interview.I'd like to ask this question from Arithmetic Progression Basics topic in division Arithmetic Progressions of Mathematics – Class 10
Answer» Correct answer is (c) 40 To EXPLAIN I would say: Here a = 9 and d = 16 – 9 = 7 Let the given AP contain n terms. Tn = 282 a + (n – 1)d = 282 9 + (n – 1)7 = 282 9 + 7n – 7 = 282 7n = 280 n = 40 Thus, the given AP has 40 terms.

Discussion

9.	What will be the 99^thterm from the end of the AP 500, 489, 478, 467… – 1139?(a) 1078(b) 1123(c) 12(d) 61The question was asked in a national level competition.This key question is from Nth Term of Arithmetic Progression topic in section Arithmetic Progressions of Mathematics – Class 10
Answer» Correct choice is (d) 61 The best explanation: In this case SINCE we have to find the 99^thterm from the END. We will consider the first term to be -1139 and the common difference will be 11 Now, a = -1139, d = 11 and n = 99 T99 = a + (n – 1)d T99 = -1139 + (99 – 1)11 T99 = -1139 + 1078 = -61 The value of 99^thterm from the end is 61.

Discussion

10.	What will be the sum of all natural numbers lying between 500 and 5000, which are divisible by 17?(a) 567898(b) 729810(c) 765835(d) 234526The question was asked by my college director while I was bunking the class.I'd like to ask this question from Sum of N Terms of Arithmetic Progression in division Arithmetic Progressions of Mathematics – Class 10
Answer» Right choice is (B) 729810 To elaborate: The AP according to the given data will be 510, 527, 544, …, 4998 Here a = 510 and d = 17 Tn = a + (n – 1)d = 4998 510 + (n – 1)17 = 4998 510 + 17n – 17 = 4998 17n = 4505 n = 265 We know that, Sn = \(\FRAC {n}{2}\) (a + l) Sn = \(\frac {265}{2}\) ((510) + 4998) Sn = 132.5(5508) = 729810

Discussion

11.	If the sum of first n terms of an AP is given by Sn = 4n^2 + 6, then its first term will be _________(a) 4(b) 3(c) 5(d) 1The question was posed to me in a national level competition.My query is from Sum of N Terms of Arithmetic Progression topic in division Arithmetic Progressions of Mathematics – Class 10
Answer» Correct choice is (a) 4 The explanation: The sum of first n terms of an AP is given by Sn = 4n^2 + 6. Substituting n by n – 1 in the given equation Sn – 1 = 4(n – 1)^2 + 6 Sn – 1 = 4n^2 – 8N + 4 + 6 Sn – 1 = 4n^2 – 8n + 10 ∴ Tn = Sn – Sn – 1 Tn = 4n^2 + 6 – (4n^2 – 8n + 10) Tn = 8n – 4 The first term will be T1 = 8(1) – 4 = 4

Discussion

12.	Which term of the AP 80, 76, 72, 68……. is the first negative term?(a) 22(b) 21(c) 23(d) 24I got this question in an interview.I'd like to ask this question from Arithmetic Progression Basics in division Arithmetic Progressions of Mathematics – Class 10
Answer» Right option is (a) 22 To EXPLAIN I would SAY: Here a = 80 and d = 76 – 80 =– 4 Let Tn be the FIRST negative term of the given AP. Tn < 0 a + (n – 1)d < 0 80 + (n – 1) – 4 < 0 80 – 4N + 4 < 0 84 < 4n n > 21 Hence the 22^th term of the given AP will be its first negative term.

Discussion

13.	Four numbers whose sum is 40 and sum of their squares is 480. What are the four numbers?(a) 4, 8, 12, and -16(b) 4, 8, 12, and 16(c) -4, 8, 12, and 16(d) 4, -8, 12, and 16The question was asked during an online interview.Asked question is from Arithmetic Progression Basics in division Arithmetic Progressions of Mathematics – Class 10
Answer» RIGHT choice is (b) 4, 8, 12, and 16 To elaborate: LET the four NUMBERS be (a + 3d), (a + d), (a – 3d), (a – d). Sum of the four numbers is 40. a + 3d + a + d + a – 3d + a – d = 40 4a = 40 a = 10 Sum of their SQUARES is 480. (a + 3d)^2 + (a + d)^2 + (a – 3d)^2 + (a – d)^2 = 480 4a^2 + 20d^2 = 480 10^2 + 5d^2 = 120 100 + 5d^2 = 120 5d^2 = 20 d^2 = 4 d = 2, -2 Hence the four numbers are 4, 8, 12, and 16.

Discussion

14.	The sum of all 2 – digit numbers divisible by 19 will be __________(a) 345(b) 245(c) 275(d) 285I got this question during an interview for a job.Enquiry is from Sum of N Terms of Arithmetic Progression topic in division Arithmetic Progressions of Mathematics – Class 10
Answer» The CORRECT option is (c) 275 For EXPLANATION I would say: The AP ACCORDING to the given data will be 19, 38, 57, …, 95 Here a = 19 and d = 19 Tn = a + (n – 1)d = 95 19 + (n – 1)19 = 95 19 + 19n – 19 = 95 19n = 95 n = 5 We know that, Sn = \(\frac {n}{2}\) (a + l) Sn = \(\frac {5}{2}\) ((19) + 95) Sn = 285

Discussion

15.	If the n^thterm of the AP is 2n + 7, then the common difference will be _____(a) -2(b) 2(c) 3(d) -3This question was posed to me by my college director while I was bunking the class.This question is from Nth Term of Arithmetic Progression in division Arithmetic Progressions of Mathematics – Class 10
Answer» RIGHT option is (b) 2 To elaborate: n^th TERM of the AP is 2n + 7 Tn = 2n + 7 Common DIFFERENCE = T2 – T1 = (2 × 2 + 7 – (2 × 1 + 7)) = 11 – 9 = 2

Discussion

16.	The sum of n terms of an AP in which first term is a, common difference is d and last term is l, is Sn = \(\frac {n}{2}\)(a + l).(a) True(b) FalseThe question was posed to me during an interview for a job.This interesting question is from Sum of N Terms of Arithmetic Progression in section Arithmetic Progressions of Mathematics – Class 10
Answer» Right answer is (a) True To explain I would say: CONSIDER an AP having N terms in which First term = a, common difference = d and last term = l. Then, l = a + (n – 1)d We may write the given AP as a, a + d, a + 2d …., (l – 2d), (l – d), l Let Sn be the SUM of the first n terms of the AP. Then, Sn = a + (a + d) + (a + 2d) … + (l – 2d) + (l – d) + l Writing the above series in reverse order, we get Sn = (l – 2d) + (l – d) + l … + a + (a + d) + (a + 2d) Adding the two EQUATIONS we get, 2Sn = a + l + (a + l) + (a + l) …n times = n(a + l) Sn = \(\frac {n}{2}\)(a + l)

Discussion

17.	What will be the n^th term of the AP 1, 5, 9, 13, 17…….?(a) 4n – 3(b) 3n – 4(c) 4n + 3(d) 3n + 4This question was posed to me in an international level competition.I want to ask this question from Nth Term of Arithmetic Progression in division Arithmetic Progressions of Mathematics – Class 10
Answer» The CORRECT option is (a) 4n – 3 For EXPLANATION: Here a = 1 and d = 4 The N^thterm of the AP = a + (n – 1)d = 1 + (n – 1)4 = 1 + 4n – 4 = 4n – 3

Discussion

18.	What will be the 14^thterm of the AP 5, 8, 11, 14, 17…….?(a) 30(b) 41(c) 40(d) 44The question was posed to me during an online interview.My doubt is from Nth Term of Arithmetic Progression in chapter Arithmetic Progressions of Mathematics – Class 10
Answer» CORRECT answer is (d) 44 The explanation is: Here a = 5, d = 8 – 5 = 3 and n = 14 T14 = a + (n – 1)d T14 = 5 + (14 – 1)3 T14 = 5 + 13 × 3 T14 = 44

Discussion

19.	What will be the sum of all 3-digit even positive numbers?(a) 247050(b) 269450(c) 269350(d) 269580I got this question in an international level competition.My question is from Sum of N Terms of Arithmetic Progression topic in portion Arithmetic Progressions of Mathematics – Class 10
Answer» CORRECT option is (a) 247050 Best explanation: The AP according to the given data will be 100, 102, 104, …, 998 Here a = 100 and d = 2 Tn = a + (n – 1)d = 998 100 + (n – 1)2 = 998 100 + 2N – 2 = 998 2n = 998 – 98 n = 450 We know that, Sn = \(\frac {n}{2}\) (a + l) Sn = \(\frac {450}{2}\) ((100) + 998) Sn = 225(100 + 998) = 247050

Discussion

20.	The sum of the first 10 terms of an AP is the same as the sum of its first 5 terms, then the sum of its 15th term will be _______(a) 1(b) 0(c) 2(d) 3The question was posed to me in semester exam.My question is based upon Sum of N Terms of Arithmetic Progression in section Arithmetic Progressions of Mathematics – Class 10
Answer» Right option is (B) 0 For explanation I would say: The SUM of the first 10 TERMS of an AP is the same as the sum of its first 5 terms S10 = S5 \(\frac {10}{2}\) (2a + (10 – 1)d) = \(\frac {5}{2}\) (2a + (5 – 1)d) 5(2a + 9d) = \(\frac {5}{2}\) (2a + 4d) 5(2a + 9d) = 5(a + 2d) (2a + 9d) = (a + 2d) 2a – a = 2d – 9d a =– 7d S15 = \(\frac {N}{2}\) (2a + (n – 1)d) = \(\frac {15}{2}\) (2a + (15 – 1)d) = \(\frac {15}{2}\) (2a + 14D) = 15(a + 7d) = 15(-7d + 7d) = 0

Discussion

21.	The sum of first 20 terms of the AP 10, 12, 14, 16, 18…. is _________(a) 200(b) 580(c) 620(d) 440This question was addressed to me in an interview for internship.The question is from Sum of N Terms of Arithmetic Progression topic in section Arithmetic Progressions of Mathematics – Class 10
Answer» Right OPTION is (b) 580 For explanation I WOULD say: Here a = 10, d = 2 and N = 20. We know that, Sn = \(\frac {n}{2}\) (2a + (n – 1)d) S20 = \(\frac {20}{2}\) (2(10) + (20 – 1)2) S20 = 10(20 + 38) = 580

Discussion

22.	If 5 times the 5^thterm of an AP is equal to 15 times its 15^thterm, then the value of its 20^thterm will be _______(a) 0(b) 1(c) 2(d) 3I got this question in an internship interview.This question is from Nth Term of Arithmetic Progression in division Arithmetic Progressions of Mathematics – Class 10
Answer» The correct CHOICE is (a) 0 For explanation I would say: 5(5^th term) = 15(15^th term) 5^th term = a + (5 – 1)d = a + 4d 15^th term = a + (15 – 1)d = a + 14d 5(a + 4d) = 15(a + 14d) 5a + 20d = 15a + 210d 20d – 210d = 15a – 5a -190d = 10a a = -19d Now, the 20^thterm = a + (20 – 1)d = a + 19d But a = -19d Hence, -19d + 19d = 0

Discussion

23.	What will be the value of k so that (2k + 1), (5k – 3) and (-8k + 5) are three consecutive terms of an AP?(a) 4(b) 3(c) \(\frac {3}{4}\)(d) \(\frac {4}{3}\)I got this question by my college director while I was bunking the class.This interesting question is from Arithmetic Progression Basics in section Arithmetic Progressions of Mathematics – Class 10
Answer» Right answer is (c) \(\frac {3}{4}\) To explain: Since, (2k + 1), (5k – 3) and (-8k + 5) are three CONSECUTIVE TERMS of an AP. The common difference will be same. (5k – 3) – (2k + 1) = (-8k + 5) – (5k – 3) 3k – 4 =-13k + 8 16k = 12 k = \(\frac {3}{4}\)

Discussion

24.	If the n^thterm of the AP is 8n + 1, then the 20^th term will be ______(a) 160(b) 120(c) 161(d) 121This question was posed to me in my homework.The doubt is from Nth Term of Arithmetic Progression topic in chapter Arithmetic Progressions of Mathematics – Class 10
Answer» The CORRECT answer is (C) 161 Best explanation: n^thterm of the AP is 8n + 1 Tn = 8n + 1 T20 = 8(20) + 1 T20 = 161

Discussion

25.	The sum of 5 numbers in AP is 10 and their product is 80. What are the five numbers?(a) 2 + 2√6, 2 + √6, 2, 2 – 2√6, 2 – √6(b) 2 + 2√6, 2 + √6, 2 – 2√6, 2 – √6(c) 2 + 2√6, 2 – √6, 2, 2 – 2√6, 2 – √6(d) 2 + 2√6, 2, 2 – 2√6, 2 – √6This question was addressed to me in semester exam.My question is from Arithmetic Progression Basics topic in section Arithmetic Progressions of Mathematics – Class 10
Answer» Right choice is (a) 2 + 2√6, 2 + √6, 2, 2 – 2√6, 2 – √6 The explanation is: Let the FIVE NUMBERS in AP be (a + 2D), (a + d), a, (a – 2d) and (a – d). Sum of the five numbers is 10. ∴ (a + 2d) + (a + d) + a + (a – 2d) + (a – d) = 10 5a = 10 a = 2 Now, product of the numbers is 80. ∴ (a + 2d)(a + d)a(a – 2d)(a – d) = 80 a^5 – 5a^3 d^2 + 4d^4 a = 80 Substituting a = 2, we get 2^5 – 5(2^3 d^2) + 4d^4 (2) = 80 32 – 40d^2 + 8d^4 = 80 8d^4 – 40d^2 – 48 = 0 Substitute d^2 = t t^2 – 5t – 6 = 0 Solving the equation, we get, t = 6, -1 Now, t = d^2 Hence, d = ±√6, ±√-1 The five numbers are 2 + 2√6, 2 + √6, 2, 2 – 2√6, 2 – √6 or 2 – 2√6, 2 – √6, 2, 2 + 2√6, 2 + √6 or 2 + 2√-1, 2 + √-1, 2, 2 – 2√-1, 2 – √-1 or 2 – 2√-1, 2 – √-1, 2, 2 + 2√-1, 2 + √-1.

Discussion

26.	If the 11^thterm of an AP is \(\frac {1}{13}\) and its 13^thterm is \(\frac {1}{11}\), then what will be the value of143^th term?(a) \(\frac {1}{143}\)(b) 1(c) 0(d) \(\frac {23}{143}\)This question was posed to me during a job interview.This intriguing question originated from Nth Term of Arithmetic Progression in chapter Arithmetic Progressions of Mathematics – Class 10
Answer» Right choice is (b) 1 For explanation: Here 11^thterm = \(\frac {1}{13}\) 13^thterm = \(\frac {1}{11}\) Let the FIRST TERM of the AP be a and COMMON difference be d T11 = a + (n – 1)d = \(\frac {1}{13}\) T11 = a + (11 – 1)d = \(\frac {1}{13}\) T11 = a + 10d = \(\frac {1}{13}\)(1) T13 = a + (n – 1)d = \(\frac {1}{11}\) T13 = a + (13 – 1)d = \(\frac {1}{11}\) T13 = a + 12D = \(\frac {1}{11}\)(2) Subtracting (1) from (2) We GET, a + 12d – (a + 10d) = \(\frac {1}{11} – \frac {1}{13}\) 2d = \(\frac {2}{143}\) d = \(\frac {1}{143}\) Now, substituting value of d in equation 1 We get, T11 = a + 10(\(\frac {1}{143}\)) = \(\frac {1}{13}\) a = \(\frac {1}{143}\) The 143^th term = \(\frac {1}{143}\) + 142\(\frac {1}{143} = \frac {(1+142)}{143} \) = 1

Discussion

27.	The sum of 50 + 100 + 150 + 200 + …….. + 1000 is _________(a) 10000(b) 14400(c) 10500(d) 12100This question was addressed to me in class test.My doubt stems from Sum of N Terms of Arithmetic Progression topic in portion Arithmetic Progressions of Mathematics – Class 10
Answer» RIGHT option is (c) 10500 Easiest explanation: Here a = 50, d = 50 and Tn = 1000. Tn = a + (n – 1)d = 1000 50 + (n – 1)50 = 1000 50 + 50n – 50 = 1000 n = 20 We know that, Sn = \(\frac {n}{2}\) (a + l) Sn = \(\frac {20}{2}\) ((50) + 1000) Sn = 10(50 + 1000) = 10500

Discussion

28.	The n^th term if an AP is 5n + 2, then the sum of first n terms of the AP will be __________(a) \(\frac {n^2 – 8}{2}\)(b) \(\frac {n^2 + 8}{2}\)(c) \(\frac {n^2 – 9}{2}\)(d) \(\frac {n^2 + 9}{2}\)I got this question during an internship interview.The question is from Sum of N Terms of Arithmetic Progression in portion Arithmetic Progressions of Mathematics – Class 10
Answer» Correct ANSWER is (d) \(\FRAC {n^2 + 9}{2}\) Explanation: n^th term = 5n + 2 Tn = 5n + 2 a = T1 = 5(1) + 2 = 7 d = T2 – T1 = 5(2) + 2 – (5 + 2) = 5 We KNOW that, Sn = \(\frac {n}{2}\) (2a + (n – 1)d) Sn = \(\frac {n}{2}\) (2(7) + (n – 1)5) Sn = 7n + \(\frac {n^2}{2} – \frac {5n}{2} = \frac {n^2 + 9}{2}\)

Discussion

29.	The middle term of the AP 11, 8, 5, …,-79 will be?(a) 30(b) -34(c) 34(d) -30This question was addressed to me in my homework.I would like to ask this question from Arithmetic Progression Basics in division Arithmetic Progressions of Mathematics – Class 10
Answer» The correct choice is (b) -34 The explanation is: Here a = 11 and d = 8 – 11 =-3 Let the given AP contain N terms. Tn = -79 a + (n – 1)d = -79 11 + (n – 1) – 3 = -79 11 – 3n + 3 =-79 14 + 79 = 3n n = 31 Thus, the given AP has 31 terms. ∴ its middle term =\(\FRAC {1}{2}\) (31 + 1) = 16^th term ∴ 16^thterm = 11 + (16 – 1) – 3 = 11 – 45 =-34

Discussion

30.	Which term of the AP 2, 11, 20, 29…… is 290?(a) 32(b) 35(c) 30(d) 33I had been asked this question in an interview for internship.My question is taken from Arithmetic Progression Basics in division Arithmetic Progressions of Mathematics – Class 10
Answer» CORRECT choice is (d) 33 For explanation I WOULD say: Here a = 2 and d = 11 – 2 = 9 Let the given AP contain n terms. Tn = 290 a + (n – 1)d = 290 2 + (n – 1)9 = 290 2 + 9N – 9 = 290 9n = 297 n = 33 Thus, the 33 term of the AP is 290.

Discussion

31.	What is the arithmetic mean between a^2 and b^2 ?(a) \(\frac {1}{2}\) (a – b)(b) \(\frac {1}{2}\) (a + b)(c) \(\frac {1}{2}\) (a^2 – b^2)(d) \(\frac {1}{2}\) (a^2 + b^2)The question was posed to me in homework.My question is based upon Arithmetic Progression Basics topic in division Arithmetic Progressions of Mathematics – Class 10
Answer» Correct choice is (d) \(\FRAC {1}{2}\) (a^2 + B^2) Explanation: We know that the arithmetic MEAN between two numbers is\(\frac {1}{2}\) (a + b) ∴ Arithmetic mean between a^2 and b^2 = \(\frac {1}{2}\) (a^2 + b^2)

Discussion

32.	A sequence in which each term differs from its preceding term by a constant is called arithmetic progression.(a) True(b) FalseI got this question in an interview for internship.This intriguing question originated from Arithmetic Progression Basics topic in section Arithmetic Progressions of Mathematics – Class 10
Answer» Right answer is (a) True Easy explanation: Consider an EXAMPLE, 8, 11, 14, 17, 20, …. Now, 11 – 8 = 3 14 – 11 = 3 Here the constant is 3. This constant is ALSO termed as common difference.

Discussion

33.	Sequences which follow a definite pattern called progressions.(a) True(b) FalseThe question was asked by my school teacher while I was bunking the class.This interesting question is from Arithmetic Progression Basics topic in portion Arithmetic Progressions of Mathematics – Class 10
Answer» CORRECT CHOICE is (a) True Explanation: Let us consider an example, 2, 4, 6, 8, … Here each term is twice the PRECEDING term. Since it FOLLOWS a definite pattern it is CALLED as progressions. Progressions are of three types: Arithmetic progression, Geometric progression and Harmonic progression.

Discussion

34.	If we add the terms of an AP, then we get a corresponding series.(a) True(b) FalseThis question was addressed to me in an internship interview.This intriguing question comes from Arithmetic Progression Basics in portion Arithmetic Progressions of Mathematics – Class 10
Answer» Correct choice is (a) True For EXPLANATION: For EXAMPLE, consider an AP 2, 11, 20, 29…… Adding the TERMS of the AP we get the arithmetic series as 2 + 11 + 20 + 29 + ⋯

Discussion

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How many terms of the AP 5,10,15,20….. must be added to get a sum of 330?(a) -11(b) -12(c) 12(d) 11The question was asked in final exam.My question is based upon Sum of N Terms of Arithmetic Progression topic in portion Arithmetic Progressions of Mathematics – Class 10

If the 7^thterm of an AP is 20 and its 11^thterm is 40 then, what will be the common difference?(a) 3(b) 4(c) 5(d) 2The question was asked in an online quiz.The query is from Nth Term of Arithmetic Progression topic in division Arithmetic Progressions of Mathematics – Class 10

If the n^thterm of the AP is 7n – 9, then the first term is ________(a) 1(b) 6(c) 3(d) 4The question was asked in quiz.This interesting question is from Nth Term of Arithmetic Progression topic in portion Arithmetic Progressions of Mathematics – Class 10

How many terms are there in the AP 9, 16, 23, 30……………282?(a) 50(b) 45(c) 40(d) 42I had been asked this question during a job interview.I'd like to ask this question from Arithmetic Progression Basics topic in division Arithmetic Progressions of Mathematics – Class 10

What will be the 99^thterm from the end of the AP 500, 489, 478, 467… – 1139?(a) 1078(b) 1123(c) 12(d) 61The question was asked in a national level competition.This key question is from Nth Term of Arithmetic Progression topic in section Arithmetic Progressions of Mathematics – Class 10

Which term of the AP 80, 76, 72, 68……. is the first negative term?(a) 22(b) 21(c) 23(d) 24I got this question in an interview.I'd like to ask this question from Arithmetic Progression Basics in division Arithmetic Progressions of Mathematics – Class 10

The sum of all 2 – digit numbers divisible by 19 will be __________(a) 345(b) 245(c) 275(d) 285I got this question during an interview for a job.Enquiry is from Sum of N Terms of Arithmetic Progression topic in division Arithmetic Progressions of Mathematics – Class 10

What will be the 14^thterm of the AP 5, 8, 11, 14, 17…….?(a) 30(b) 41(c) 40(d) 44The question was posed to me during an online interview.My doubt is from Nth Term of Arithmetic Progression in chapter Arithmetic Progressions of Mathematics – Class 10

What will be the sum of all 3-digit even positive numbers?(a) 247050(b) 269450(c) 269350(d) 269580I got this question in an international level competition.My question is from Sum of N Terms of Arithmetic Progression topic in portion Arithmetic Progressions of Mathematics – Class 10

The sum of first 20 terms of the AP 10, 12, 14, 16, 18…. is _________(a) 200(b) 580(c) 620(d) 440This question was addressed to me in an interview for internship.The question is from Sum of N Terms of Arithmetic Progression topic in section Arithmetic Progressions of Mathematics – Class 10

If the n^thterm of the AP is 8n + 1, then the 20^th term will be ______(a) 160(b) 120(c) 161(d) 121This question was posed to me in my homework.The doubt is from Nth Term of Arithmetic Progression topic in chapter Arithmetic Progressions of Mathematics – Class 10

The sum of 50 + 100 + 150 + 200 + …….. + 1000 is _________(a) 10000(b) 14400(c) 10500(d) 12100This question was addressed to me in class test.My doubt stems from Sum of N Terms of Arithmetic Progression topic in portion Arithmetic Progressions of Mathematics – Class 10

The middle term of the AP 11, 8, 5, …,-79 will be?(a) 30(b) -34(c) 34(d) -30This question was addressed to me in my homework.I would like to ask this question from Arithmetic Progression Basics in division Arithmetic Progressions of Mathematics – Class 10

Which term of the AP 2, 11, 20, 29…… is 290?(a) 32(b) 35(c) 30(d) 33I had been asked this question in an interview for internship.My question is taken from Arithmetic Progression Basics in division Arithmetic Progressions of Mathematics – Class 10

Sequences which follow a definite pattern called progressions.(a) True(b) FalseThe question was asked by my school teacher while I was bunking the class.This interesting question is from Arithmetic Progression Basics topic in portion Arithmetic Progressions of Mathematics – Class 10

If we add the terms of an AP, then we get a corresponding series.(a) True(b) FalseThis question was addressed to me in an internship interview.This intriguing question comes from Arithmetic Progression Basics in portion Arithmetic Progressions of Mathematics – Class 10