Question

The arithmetic sequence `a_i` is defined by the formula `a_1=15` and `a_i = a_(i-1) - 7`. What is the sum of the first 660 terms in the sequence?

Answer 1

Sum of first `660` term is `-1512390`

Explanation:

Sum of an arithmetic sequence upto `n` terms, whose first term is `a_1` and common difference `a_i-a_(i-1)=d`, is

`n/2(2a_1+(n-1)d`.

Here `a_1=15` and `d=a_i-a_(i-1)=-7` sum of first `660` term is

`660/2(2×15+(660-1)×(-7))`

= `330×(30-659×7)`

= `330×(30-4613)`

= `330×(-4583)`

= `-1512390`