Question

the arithmetic sequence ai is defined by the formula: a1 = -53 ai = ai-1 + 6 find the sum of the first 880 terms in the sequence

Answer 1

The sum of the first 880 terms in the sequence is 2,273,920.

Explanation:

Arithmetic sequence:

The difference between consecutive terms is always the same, called common difference, and the nth term is given by:

`a_(n) = a_0 + (n-1)d`

In which d is the common difference.

Sum of the first n terms:

The sum of the first n terms of an arithmetic sequence is given by:

`S_(n) = (n(a_1+a_n))/(2)`

ai = ai-1 + 6

This means that
`d = 6`

In this question:

Sum of the first 800 terms, so
`n = 800`

First term is -53, so
`a_1 = -53`

The 880th term is:

`a_(880) = -53 + (880-1)*6 = 5221`

Sum

`S_(n) = (880(-53+5221))/(2) = 440(-53+5221) = 2273920`

The sum of the first 880 terms in the sequence is 2,273,920.