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:
[tex]S=\frac{n}{2} [2a_{1}+(n-1)r][/tex]
where
n is how many terms to add
a₁ is the 1st term of the sequence
r is the constant
For the sequence above:
[tex]S=\frac{17}{2} [2(5)+(17-1)1][/tex]
[tex]S=\frac{17}{2}(26)[/tex]
[tex]S=17(13)[/tex]
S = 221
The sum of the first 17 terms of the arithmetic sequence {5,6,7,8,9,10...} is 221
