Question

Find the sum of the series -11 - 3 + 5 + 13 + ... + 125 using the series formula.

Answer 1

1026

Explanation:

Common difference = d = 2nd term - first term

d = -3 - (-11) = -3 +11 = 8

First term = a = -11

First we need to find the number of terms in this series

`a_(n) = 125\\\\a + (n- 1)d = a_(n)\\\\`

-11 + (n- 1) * 8 = 125

(n-1)*8 = 125 + 11

(n-1) * 8 = 136

n -1 = 136/8

n -1 = 17

n = 17+1

n = 18

`S_(n) =(n)/(2)(a+a_(n))\\\\S_(18) =(18)/(2)(-11+125)\\\\`

= 9 * 114

= 1026