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Question
Find the rth term of an A.P. sum of whose first n terms is 2n + 3n2
Solution
Given that Sn = 2n + 3n2
⇒ S1 = 2 × 1 + 3(1)2 = 5
⇒ S2 = 2 × 2 + 3 × 4 = 16
⇒ S3 = 2 × 3 + 3 × 9 = 33
… … …
∴ S1 = a1 = 5
S2 – S1 = a2
= 16 – 5
= 11
∴ d = a2 – a1
= 11 – 5
= 6
Now Tr = a1 + (r – 1)d
= 5 + (r – 1)6
= 5 + 6r – 6
= 6r – 1
Hence, the required rth term is 6r – 1.
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