Question 35. In an A.P. , the first term is 2, the last term is 29 and the sum of the terms is 155. Find the common difference of the A.P.

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deepaksoniGuru

Asked: June 30, 20212021-06-30T20:57:27+05:30 2021-06-30T20:57:27+05:30In: CBSE

This is the basic and conceptual question from Chapter name- Arithmetic Progression
Chapter number- 9
Exercise 9.6

In this question we have been given that In an A.P. , the first term is 2, the last term is 29 and the sum of the terms is 155.

Now we have to find the common difference of the A.P.

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Question 35

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AAREKH · Answer 1 · 2021-07-14T15:20:39+05:30

AAREKH Guru

Given A.P. has first term(a) = 2, last term(a_n) = 29 and sum(S_n) = 155.

By using the formula of the sum of first n terms of an A.P.

S_n = n[a + a_n] / 2.

=> 155 = n(2 + 29) / 2

=> 31n = 310

=> n = 10

By using the formula of nth term of an A.P.

a_n = a + (n – 1)d

So,

=> 29 = 2 + (10 – 1)d

=> 9d = 27

=> d = 3

Hence, the common difference of the A.P. is 3.