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Question
The sum of the first n terms of an AP is (3n2+6n) . Find the nth term and the 15th term of this AP.
Solution
Let Sn denotes the sum of first n terms of the AP.
∴ sn = 3n2 + 6n
⇒ `s_(n-1 )= 3 (n-1)^2 + 6 (n-1)`
= 3 ( n2 - 2n + 1) + 6 (n-1)
= 3n2 - 3
∴ nth term of the AP , an
= sn = sn-1
= (3n2 + 6n) - ( 3n2 -3)
= 6n + 3
Putting n=15,we get
a15 = 6 × 15 + 3 = 90 + 3 = 93
Hence, the nth term is (6n + 3) and 15th term is 93.
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