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nth Term of A.P

If sum of n o...

Question

If sum of $n$ of a series is given by $S_{n} = 3 n^{2} + 3 n$ , then $n^{t h}$ term of the series is

A

3 n

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B

3 n + 10

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C

6 n

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D

6 n + 10

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Solution

The correct option is C $6 n$
Given : $S_{n} = 3 n^{2} + 3 n$
Now,
$T_{n} = S_{n} - S_{n - 1} \Rightarrow T_{n} = 3 n^{2} + 3 n - (3 (n - 1)^{2} + 3 (n - 1)) \Rightarrow T_{n} = 3 n^{2} + 3 n - (3 (n^{2} - 2 n + 1) + 3 n - 3) \Rightarrow T_{n} = 3 n^{2} + 3 n - (3 n^{2} - 3 n) ∴ T_{n} = 6 n$

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nth Term of A.P

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