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Question

Find the sum of first 24 terms of the A.P. whose nth term is given by an=3+2n


A

568

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B

624

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C

564

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D

672

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Solution

The correct option is D

672


As an=3+2n,

so,

a1=3+2×1=5

a2=3+2×2=7

a3=3+2×3=9

List of numbers becomes 5, 7, 9, 11 . . .

Here, 75=97=119=2 and so on.

So, it forms an AP with common difference d=2.

To find S24, we have n=24, a=5, d=2.

Therefore, S24=242(2(5)+(241)2)

=12(10+46)=672


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