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:(vii) k, if Sn = 3n2 + 5n and ak = 164.

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deepaksoniGuru

Asked: July 1, 20212021-07-01T08:03:13+05:30 2021-07-01T08:03:13+05:30In: CBSE

This is an arithmetic progression based question from Chapter name- Arithmetic progressions

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 k, if Sn = 3n2 + 5n and ak = 164

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Question no 56(vii)

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AAREKH · Answer 1 · 2021-07-01T10:04:57+05:30

AAREKH Guru

Given S_n = 3n² + 5n,

On putting n = 1, we get the first term(a), S₁ = a = 3(1)²+ 5(1) = 8

On putting n = 2 gives S₂ = a + a + d = 3(2)²+ 5(2) = 22

=> d = 22 – 2a

=> d = 22–16 = 6

The kth term of the A.P., a_k = a + (k – 1)d = 164

=> 8 + (k – 1)6 = 164

=> 6k = 162

=> k = 27

Hence, the value of k is 27.