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Sequence and Series

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Question : 18 of 86

Marks: +1, -0

The nth term of series whose sum to n terms is

5 n^{2}+2 n

is

$5 n+3$
$10 n-2$
$5 n+2$
$10 n-3$

Solution:

Concept:

The

n

th term

T_n

of a sequence is the difference between the sum of

n

terms

S_n

and the sum of

n-1

terms

S_{n-1}

:

T_n = S_n - S_{n-1}

.

Explanation:

Given

S_n = 5n^2 + 2n

.

First find

S_{n-1}

: replace

n

by

n-1

.

S_{n-1} = 5(n-1)^2 + 2(n-1) = 5(n^2 - 2n + 1) + 2n - 2 = 5n^2 - 10n + 5 + 2n - 2 = 5n^2 - 8n + 3

.

Now

T_n = S_n - S_{n-1} = (5n^2 + 2n) - (5n^2 - 8n + 3) = 5n^2 + 2n - 5n^2 + 8n - 3 = 10n - 3

.

Answer:

The

n

th term is

10n - 3

, which corresponds to option D.

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