Question

The arithmetic sequence ai is defined by the formula: a 1 =15 a i =a i-1 -7 Find the sum of the first 660 terms in the sequence.

Answer 1

The sum of the first 660 terms in the sequence=−1512390

Explanation:

We are given that an arithmetic sequence

`a_1=15`

`a_(i)=a_(i-1)-7`

We have to find the sum of first 660 terms

Substitute i=2

`a_2=a_1-7=15-7=8`

Substitute i=3

`a_3=a_2-7=8-7=1`

Now, the common difference

`d=a_2-a_1=8-15=-7`

Now, sum of n terms of an A.P

`S_n=(n)/(2)(2a+(n-1)d)`

Substitute n=660, d=-7, a=15

`S_(660)=(660)/(2)(30+(660-1)(-7))`

`S_(660)=-1512390`

Hence, the sum of the first 660 terms in the sequence=−1512390