Question

For the arithmetic sequence beginning with the terms {5, 6, 7, 8, 9, 10...}, what is the sum of the first 17 terms

Answer 1

Answer: S = 221

Step-by-step explanation: An arithmetic sequence is a set of numbers in order, having the difference between one term and the next a constant.

The sum of an arithmetic sequence can be calculated as the following formula:

$S=\frac{n}{2} [2a_{1}+(n-1)r]$

where

n is how many terms to add

a₁ is the 1st term of the sequence

r is the constant

For the sequence above:

$S=\frac{17}{2} [2(5)+(17-1)1]$

$S=\frac{17}{2}(26)$

$S=17(13)$

S = 221

The sum of the first 17 terms of the arithmetic sequence {5,6,7,8,9,10...} is 221