Question

Sum to n terms of an arithmetic progression is 2n2 + n then eighth term is 31?

Answer 1

Answer:

Eighth term of given A.P=$31$

Step-by-step explanation:

Given Sum of n terms $S_{n}=2n^{2}+n$---(1)

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We know that,

$\boxed {t_{n}=S_{n}-S_{n-1}}$

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i ) Substitute n = 8 in (1), we get

$S_{8} = 2\times 8^{2}$

= $2\times 64+8$

=$128+8$

=$136$----(2)

ii) Substitute n=7 in equation (1), we get

$S_{7} = 2\times 7^{2}+7$

= $2\times 49+7$

=$98+7$

=$105$-----(3)

iii)Now , Eighth term of given A.P:

$t_{8} = S_{8}-S_{(8-1)}$

= $136-105$

=$31$

Therefore,

Eighth term of given A.P=$31$

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