MATH SOLVE

4 months ago

Q:
# What is the sum of the first 21 terms of this arithmetic series?-5+(-3)+(-1)+1+...

Accepted Solution

A:

Answer:[tex]S_{21}=315[/tex]Step-by-step explanation:The given arithmetic series is -5+(-3)+(-1)+1+...The first term of this series is [tex]a_1=-5[/tex] The common difference is [tex]d=-3--5[/tex][tex]d=-3+5[/tex][tex]d=2[/tex]The sum of the first n-terms of an arithmetic sequence is [tex]S_n=\frac{n}{2}(2a+d(n-1))[/tex][tex]S_{21}=\frac{21}{2}(2(-5)+2(21-1))[/tex][tex]S_{21}=\frac{21}{2}(-10+2(20))[/tex][tex]S_{21}=\frac{21}{2}(-10+40)[/tex][tex]S_{21}=\frac{21}{2}(30)[/tex][tex]S_{21}=(21)(15)[/tex][tex]S_{21}=315[/tex]