Respuesta :
Answer:
The sum of the arithmetic sequence is [tex]S_{8}=-324[/tex].
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 [tex]a_1[/tex] and the common difference is d, then the nth term of the sequence is given by:
[tex]a_{n}=a_{1}+(n-1)d[/tex]
For the sequence
[tex]-2,-13,-24,-35,...[/tex]
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, [tex]a_1[/tex] and last term, [tex]a_n[/tex], divide by 2 in order to get the mean of the two values and then multiply by the number of values, n
[tex]S_{n}=\frac{n}{2}(a_{1}+a_{n})[/tex]
The sum of the arithmetic sequence is
[tex]a_{8}=-2+(8-1)(-11)=-2-77=-79[/tex]
[tex]S_{8}=\frac{8}{2}(-2-79})=4\left(-2-79\right)=4\left(-81\right)=-324[/tex]
