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

Answer:

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

Step-by-step 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

$S_n=\frac{n}{2}(2a+(n-1)d)$

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

$S_{660}=\frac{660}{2}(30+(660-1)(-7))$

$S_{660}=-1512390$

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