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in Arithmetic Progression by (48.8k points)
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In an AP, if Sn = 3n2 + 5n and ak = 164, then find the value of k.

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Sn = 3n2 + 5n

Sn - 1 = 3(n - 1)2 + 5(n - 1)

= 3(n2 - 2n + 1) + 5n - 5

= 3n2 - 6n + 3 + 5n - 5

= 3n2 - n - 2

Sn - Sn - 1 = 3n2 + 5n - (3n2 - n - 2)

(a1 + a2 + a3 + - - - + an - 1 + an) - (a1 + a2 + a3 + - - - + an - 1) = 6n + 2

an = 6n + 2

then

ak = 6k + 2 = 164

6k = 164 - 2 = 162

k = 27

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