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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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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

CBSE DHANPAT RAI PUBLICATIONS
Understanding CBSE Mathematics
Class :- 10th
Question no 56(vii)

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1 Answer

  1. Given Sn = 3n2 + 5n,

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

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

    => d = 22 – 2a

    => d = 22–16 = 6

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

    => 8 + (k – 1)6 = 164

    => 6k = 162

    => k = 27

    Hence, the value of k is 27.

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