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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Understanding CBSE Mathematics
Class :- 10th
Question no 56(vii)
Given Sn = 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., ak = a + (k – 1)d = 164
=> 8 + (k – 1)6 = 164
=> 6k = 162
=> k = 27
Hence, the value of k is 27.