InterviewSolution
Saved Bookmarks
InterviewSolution
| 1. |
Write the sequence with nth term:(i) an = 3 + 4n(ii) an = 5 + 2n(iii) an = 6 - n(iv) an = 9 - 5nShow that all of the above sequences form A.P. |
|
Answer» (i) Put n = 1 A1 = 3 + 4(1) = 7 Put n = 2 A2 = 3 + 4(2) = 11 Put n = 3 A3 = 3 + 4(3) = 15 Common difference, d1 = a2 – a1 = 11 – 7 = 4 Common difference, d2 = a3 – a2 = 15 – 11 = 4 Since, d1 = d2 Therefore, it’s an A.P. with sequence 7, 11, 15,… (ii) Put n = 1 A1 = 5 + 2(1) = 7 Put n = 2 A2 = 5 + 2(2) = 9 Put n = 3 A3 = 5 + 2(3) = 11 Common difference, d1 = a2 – a1= 9 – 7 = 2 Common difference, d2 = a3 – a2= 11 – 9 = 2 Since, d1 = d2 Therefore, it’s an A.P. with sequence 7, 9, 11,… (iii) Put n = 1 A1 = 6 – 1 = 5 Put n = 2 A2 = 6 – 2 = 4 Put n = 3 A3 = 6 – 3 = 3 Common difference, d1 = a2 – a1= 4 – 5 = -1 Common difference, d2 = a3 - a2= 3 – 4 = -1 Since, d1 = d2 Therefore, it’s an A.P. with sequence 5, 4 , 3,… (iv) Put n = 1 A1 = 9 – 5(1) = 4 Put n = 2 A2 = 9 – 5(2) = -1 Put n = 3 A3 = 9 – 5(3) = -6 Common difference, d1 = a2 – a1 = -1 – 4 = -5 Common difference, d2 = a3 – a2 = - 6 – (-1) = - 5 Since, d1 = d2 Therefore, it’s an A.P. with sequence 4, -1, -6,… |
|