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Question
The sum of the first n terms of an A.P. is 3n2 + 6n. Find the nth term of this A.P.
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Solution
Given: Sn = 3n2 + 6n
We know that the nth term of an A.
∴ an = Sn − Sn−1
Sn−1 = 3(n − 1)2 + 6(n − 1)
= 3(n2 − 2n + 1) + 6n − 6
= 3n2 − 6n + 3 + 6n − 6
= 3n2 − 3
∴ an = Sn − Sn−1
= (3n2 + 6n) − (3n2 − 3)
= 3n2 + 6n − 3n2 + 3
= 6n + 3
Thus, nth term of this A.P. is 6n + 3.
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