Question 27. The first and the last terms of an A.P are 5 and 45 respectively. If the sum of all its terms is 400, find its common difference.

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deepaksoniGuru

Asked: June 30, 20212021-06-30T18:58:40+05:30 2021-06-30T18:58:40+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 the first and the last terms of an A.P are 5 and 45 respectively.

Also it is given that the sum of all its terms is 400,

Now we have to find its common difference

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Question 27

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AAREKH · Answer 1 · 2021-07-14T15:33:26+05:30

AAREKH Guru

Given A.P. has first term(a) = 5, last term(a_n) = 45 and sum(S_n) = 400.

Now by using the formula of sum of n terms of an A.P.

S_n = n[a + a_n] / 2

=> 400 = n[5 + 45]/2

=> 25n = 400

=> n = 16

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

a_n = a + (n – 1)d

So,

=> 45 = 5 + (16 – 1)d

=> 15d = 40

=> d = 8/3

Hence, the common difference of the given A.P. is 8/3.