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Formula for Sum of n Terms of an AP

The sum of n ...

Question

The sum of n terms of an A.P is 3n² + 5n. Find the A.P Hence it's 15^th term.

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Solution

S = 3n^2 + 5n

S1 = a1 = 3 + 5 = 8

S2 = a1 + a2 = 12 + 10 = 22

⇒ a2 = S2 - S1 = 22 - 8 = 14

S3 = a1 + a2 + a3 = 27 + 15 = 42

⇒a3 = S3 - S2 = 42 - 22 = 20

∴ Given AP is 8,14,20,.....

Thus a = 8 , d = 6
15th term is
=8+(15-1)6=8+146=8+84=92

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