(a) Find the sum of first 30 terms of AP :- 30, -24, -18, .... (b) In

1.	(a) Find the sum of first 30 terms of AP :- 30, -24, -18, .... (b) In an AP if Sn = n (4n + 1), then find the AP.
Answer» (a) a₁ = -30, a₂ = -24 d = a₂ - a₁ = -24 - (-30) = 6 \(\therefore\) sum of first 30 terms is S₃₀ = 30/2 [2a + (30 - 1)] = 15 [2 x -30 + 29 x 6] = 15 [-60 + 174] = 15 x 114 = 1710 (b) Given sum of n terms of A.P. is S_n = n(4n + 1) T₁ = S₁ = 1(4 + 1) = 5 T₂ = S₂ - S₁ = 2(4 x 2 + 1) - 5 = 18 - 5 = 13 T3 = S₃ - S₂ = 3(4 x 3 + 1) - 18 = 39 -18 = 21 T₄ = S₄ - S₃ = 4(4 x 4 + 1) - 39 = 68 - 39 = 29 Hence, required AP is 5, 13, 21, 29.....

(a) Find the sum of first 30 terms of AP :- 30, -24, -18, .... (b) In an AP if Sn = n (4n + 1), then find the AP.

Answer»

(a) a₁ = -30, a₂ = -24

d = a₂ - a₁ = -24 - (-30) = 6

\(\therefore\) sum of first 30 terms is

S₃₀ = 30/2 [2a + (30 - 1)]

= 15 [2 x -30 + 29 x 6]

= 15 [-60 + 174]

= 15 x 114

= 1710

(b) Given sum of n terms of A.P. is

S_n = n(4n + 1)

T₁ = S₁ = 1(4 + 1) = 5

T₂ = S₂ - S₁ = 2(4 x 2 + 1) - 5 = 18 - 5 = 13

T3 = S₃ - S₂ = 3(4 x 3 + 1) - 18 = 39 -18 = 21

T₄ = S₄ - S₃ = 4(4 x 4 + 1) - 39 = 68 - 39 = 29

Hence, required AP is 5, 13, 21, 29.....

Discussion

No Comment Found

Related InterviewSolutions

What is meant by coagulation of a colloidal solution? Describe briefly any three methods by which coagulation of lyophobic sols can be carried out.
What is meant by coagulation of a colloidal solution? Name any method by which coagulation of lyophobic sols can be carried out.
Classify the following contraceptives measures into different methods of birth control.(1) Vasectomy(2) tubectomy(3) Saheli(4) Diaphragms(5) Cervical caps(6) Condoms
An object is placed at a distance of 30 cm from a concave lens of focal length 15 cm. List four characteristics (nature, position etc) of the image formed by the lens.
Explain the following: (i) CH3COOH is a weak acid. (ii) Propene undergoes addition reaction. (iii) The gas stoves have inlets for air.
Accumulation of harmful chemicals in our body can be avoided. Explain how this can be achieved ?
State the changes that take place in the uterus when: (i) Implantation of embryo has occurred (ii) Female gamete/egg is not fertilised
A hollow metal sphere of radius 5cm is charged such that the potential on its surface is 10V. What is the potential at the centre of the sphere?
Ms. Raveena Sen is an IT expert and a freelancer. She recently used her skills to access the Admin password for the network server of Super Dooper Technology Ltd. and provided confidential data of the organization to its CEO, informing him about the vulnerability of their network security. Out of the following options (i) to (iv), which one most appropriately defines Ms. Sen? Justify the reason for your chosen option: (i) Hacker (ii) Cracker (iii) Operator (iv) Network Admin
An elevator descends into a mine shaft at the rate of 6 m/min. If the descent starts from 10 above the ground level, how long will it take to reach -350 m?

(a) Find the sum of first 30 terms of AP :- 30, -24, -18, .... (b) In an AP if Sn = n (4n + 1), then find the AP.

Discussion

No Comment Found

Related InterviewSolutions

Reply to Comment