Question 56. Let there be an A.P. with first term a and common difference d. If an denotes its nth term and Sn is the sum of first n terms, then find:(iii) d, if a = 3, n = 8 and Sn = 192

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deepaksoniGuru

Asked: July 1, 20212021-07-01T07:51:13+05:30 2021-07-01T07:51:13+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 there be an A.P.

first term a and common difference d.

Also, If an denotes its nth term and Sn is the sum of first n terms,

Now we have to find d, if a = 3, n = 8 and Sn = 192

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Class:- 10th
Solutions of CBSE Mathematics
Question 56(iii)

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AAREKH · Answer 1 · 2021-07-01T10:08:06+05:30

AAREKH Guru

Given A.P. has a = 3, n = 8 and S_n= 192.

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

S_n = n[2a +(n – 1)d] / 2

So,

=> 192 = 8[2(3) + (8 – 1)d] / 2

=> 4[6+7d] = 192

=> 6+7d = 48

=> 7d = 42

=> d = 6

Hence, the value of d is 6.