How do you find the sum of the arithmetic series $Sigma(2-3n)$ from n=1 to 5?

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Answer 1 · 2017-10-19T18:39:18

$Sum = -35$

Formula for sum of n terms in A.P
$Sum = n(a_1 + a_n) = (n/2)(2a_1 + (n-1) * d)$

First term $a_1 = 2-(3*1) = -1$
Second term $a_2 = 2 -(3*2) = -4$
$d = a_2 - a_1 = -4 - (-1 ) = -3$
$n = 5$

$Sum = (5/2)[(2*(-1)) + (5-1) *(-3)]$

$Sum = (5/2)[-2 + 4*(-3)] = (5/2)[-2-12] = -35$

How do you find the sum of the arithmetic series Sigma(2-3n)Sigma(2-3n) from n=1 to 5?