Question

What's the sum of ten terms of a finite arithmetic series if the first term is 13 and the last term is 89?

Answer 1

The sum of the n first terms in an arithmetic series is given by the following formula

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

Where a_1 represents the first term, a_n represents the n-th term, and n the amount of terms we want to sum.

The first term of our sequence is 13, the tenth term is 89 and the amount of terms is 10. Plugging those values in our formula, we have

$S_{10}=10\cdot(\frac{13+89}{2})=10\cdot51=510$

This sum is equal to 510.