Answer:
The sum of the sequence is -152250.
Step-by-step explanation:
Given : Sequence [tex]-32+(-34)+(-36)+...+(-778)+(-780)[/tex]
To find : What is the sum of the sequence?
Solution :
The given sequence is in Arithmetic sequence as the difference between them is same.
Where, the first term is a=-32
The common difference is [tex]d=a_2-a_1[/tex]
[tex]d=(-34)-(-32)[/tex]
[tex]d=-34+32[/tex]
[tex]d=-2[/tex]
The last term is l=-780.
The last term formula is [tex]l=a+(n-1)d[/tex]
[tex]-780=-32+(n-1)(-2)[/tex]
[tex]\frac{-780+32}{-2}=n-1[/tex]
[tex]374=n-1[/tex]
[tex]n=375[/tex]
The sum of n terms formula is
[tex]S_n=\frac{n}{2}[a+l][/tex]
[tex]S_{375}=\frac{375}{2}[-32+(-780)][/tex]
[tex]S_{375}=\frac{375}{2}[-812][/tex]
[tex]S_{375}=375\times (-406)[/tex]
[tex]S_{375}=-152250[/tex]
Therefore, the sum of the sequence is -152250.
