Question

if the sum of first m terms of an AP is 2m square +3m ,then what is its second term ?

Answer 1

Sn  - S (n-1) = an
So, a2 = S2 - S1
a2 = {2(2)^2 + 3 x2 } - { 2( 1)^2 + 3 x 1}
a2 = ( 8 + 6) - ( 2 + 3)
a2 = 14 - 5
a2 = 9

Therefore the 2nd term is 9

Answer 2

Answer:

Second term in given A.P = 9

Explanation:

Given sum of first m terms of an AP $S_{m}$= $2m^{2}+3m$

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We know that,

$n^{th} \: term \: a.p (t_{n})$

= $S_{n}-S_{n-1}$

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i)S1 = 2×1² + 3×1 = 2+3 = 5 ---(1)

ii) S2 = 2×2²+3×2 = 8+6 = 14--(2)

Here , n = 2

$t_{2}= S_{2}-S_{2-1}$

$\implies t_{2}= S_{2}-S_{1}$

$\implies t_{2}=14-5$

/* From (1) & (2) */

$\implies t_{2} = 9$

Therefore,

Second term in given A.P = 9

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