If the sum of n terms of an A.P. is $n^{2} + 2 n$ , find the 5th term of the A.P.

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Solution

The correct option is B 23
Since, sum of n terms is $n^{2} + 2 n$
If the series has only only 1 term, the sum is $1^{2} + 2 * 1 = 3$
So $t_{1} = 3$
If the series has 2 terms, the sum is $2^{2} + 2 * 2 = 8$
So $t_{2} = 8$
Common difference, $d = (t_{2} - t_{1}) = 5$
So the general term of AP would be $t_{1} + (n - 1) d = 3 + (n - 1) 5$
For the fifth term, $3 + (5 - 1) 5 = 23$

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