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

Answer:

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

Step-by-step 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:

$S_{n} = \frac{n(a_1+a_n)}{2}$

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

$S_{n} = \frac{880(-53+5221)}{2} = 440(-53+5221) = 2273920$

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