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

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