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:(v) n and d if a = 8, an = 62 and Sn = 210

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deepaksoniGuru

Asked: July 1, 20212021-07-01T07:58:01+05:30 2021-07-01T07:58:01+05:30In: CBSE

This is an arithmetic progression based 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 n and d if a = 8, an = 62 and Sn = 210

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Question no 56(v)

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AAREKH · Answer 1 · 2021-07-01T10:06:37+05:30

AAREKH Guru

Given A.P. has a = 8, a_n= 62 and S_n= 210.

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

S_n = n[a + a_n] / 2

So,

=> 210 = n[8 + 62] / 2

=> 70n = 420

=> n = 6

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

a_n = a + (n – 1)d

So,

=> 62 = 8 + (6 – 1)d

=> 5d = 54

=> d = 54/5

Hence, the value of n is 6 and d is 54/5.