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Question
In an A.P., if Sn = 3n2 + 5n and ak = 164, find the value of k.
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Solution
∵ nth term of an AP,
an = Sn – Sn – 1
= 3n2 + 5n – 3(n – 1)2 – 5(n – 1) ...[∵ Sn = 3n2 + 5n (Given)]
= 3n2 + 5n – 3n2 – 3 + 6n – 5n + 5
⇒ an = 6n + 2 ...(i)
or ak = 6k + 2 = 164 ...[∵ ak = 164 (Given)]
⇒ 6k = 164 – 2 = 162
∴ k = 27
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