Question

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

Answer 1

`S_(30)= - 3390`

Step-by-step 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= (n)/(2) ( a_(1) + l)`

The sum of the first 30 terms is given by:

`S_(30)= (30)/(2) ( 3 + - 229)`

`S_(30)=15( - 226)`

`S_(30)= - 3390`