Question

Consider the arithmetic series:

-6 + 4 + 14 + 24 + ...

Write a formula for the sum of the first n terms in this series.

A. 10n+10

B. 10n+4

C. 5n^2−11n

D. 5n^2−11

Answer 1

This is an arithmetic series, so
a(n)=a(1)+d(n-1)
a(1)= - 6
d=14-4=10
d=10
a(n)=-6+10(n-1)
a(n)=-6+10n-10*1= - 16+10n

S(n)=(n/2)*(a(1)+a(n))

S(n)=(n/2)*(-6 - 16+10n) = (n/2)*(-22+10n)=-11n+5n²

S(n)=5n²-11n
Answer is C. S(n)=5n²-11n