Question

What is the sum of the numbers in the series? 15 + 11 + 7 + . . . + (–129)

Answer 1

Using Gauss's method
Total number of terms = [15-(-129)]/4+1=36+1=37
Add
S=15+11+7+....-125-129
S=-129-125-...+7+11+15
--------------------------------
2S=-114-114-114...(37 times)
=>
sum=S=(1/2)*(-114)*37=-2109


Using AP, T(n)=15+11+7+....-129
T(n)=19-4n  => T(1)=15, T(37)=-129
S(n)=(1/2)(37)(T(1)+T(37)=(1/2)37(15-129)=2109