Find the sum of the following arithmetic series.

13+11+9+...+(-25)

Someone help please. Thanks

2 answers

well, in general for arithmetic sequence

sum from k = 0 to k = n-1
of a+kd
is
(n/2)[ 2a+(n-1)d ]
In this problem
a = 13
d = -2
now what is n?
13 + k(-2) = -25
-2 k = - 38
k = 19 for the last term
so n-1 = 19
n = 20
so we have
(20/2)[26 +19(-2)]