Question

Find the indicated sum of each sequence S8 of -2,-13,-24,-35

Answer 1

Answer:

The sum of the arithmetic sequence is $S_{8}=-324$.

Step-by-step explanation:

A sequence is a set of numbers that are in order.

In an arithmetic sequence the difference between one term and the next is a constant.  In other words, we just add the same value each time infinitely.

If the first term of an arithmetic sequence is $a_1$ and the common difference is d, then the nth term of the sequence is given by:

                                                  $a_{n}=a_{1}+(n-1)d$

For the sequence

                                                $-2,-13,-24,-35,...$

The pattern is continued by adding -11 to the last number each time.

An arithmetic series is the sum of an arithmetic sequence.  We find the sum by adding the first, $a_1$ and last term, $a_n$, divide by 2 in order to get the mean of the two values and then multiply by the number of values, n

                                                    $S_{n}=\frac{n}{2}(a_{1}+a_{n})$

The sum of the arithmetic sequence is

$a_{8}=-2+(8-1)(-11)=-2-77=-79$

$S_{8}=\frac{8}{2}(-2-79})=4\left(-2-79\right)=4\left(-81\right)=-324$