Question

If for an AP the sum of its n terms is
$S_{n} = 2n {}^{2} + 6n$
then the 2nd term of the Progression is?
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Answer 1

Given,

S, sum of first n terms of an AP

$ap = 2n {}^{2} + 3n = {5}n$

To find the common difference,

We know that sum of n terms of an AP is 5

$5 = \binom{2}{2} (a + n - 1) d$

$51=a{a= first \: \: term \: of AP}$

$2 ({1})^{2} + 3(1) = a$

$a = 5$

$\sqrt[5]{2} = =a+a+d$

$2 ({2})^{2} = +3(2)=5+5+d$

$d = 4$

Therefore common difference is equal to 4

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