Question

What is the sum of the series 3,---5,-13..........-229

Answer 1

ANSWER

$S_{30}= - 3390$

EXPLANATION

The given sequence is

3,-5,-13,.....-229.

The first term of this sequence is

a_1=3

There is a common difference of

$d = - 5 - 3 = - 8$

The last term of this sequence is -229.

The nth term of this sequence is given by:

$a_n=a_1+d(n-1)$

We use the last term to determine the number of terms in the sequence.

$- 229 = 3 + - 8(n - 1)$

$- 229 - 3= - 8(n - 1)$

$- 232= - 8(n - 1)$

Divide through by -8;

$29= (n - 1)$

$n = 30$

Hence there are thirty terms in the sequence.

The sum of the first n terms is given by:

$S_n= \frac{n}{2} ( a_{1} + l)$

The sum of the first 30 terms is given by:

$S_{30}= \frac{30}{2} ( 3 + - 229)$

$S_{30}=15( - 226)$

$S_{30}= - 3390$