In an A.P, if $ S_{n} = 3n^2 + 5n $ and $ a_k = 164 $
Arithmetic Progressions (10)In an A.P, if $ S_{n} = 3n^2 + 5n $ and $ a_k = 164 $, find the value of k
Answer
Sn = 3n2 + 5n
n = 1, S1 (1st term) = 3(1)2 + 5(1) = 8
n = 2, S2 (sum of 1st two terms) = 3(2)2 + 5(2) = 22
a1 + a2 = 22
⇒ a2 = 22 - 8 = 14
d = a2 – a1 = 14 – 8 = 6
ak = 164
⇒ 8 + (k - 1)6 = 164
k = 27
Exam Year:
2023
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