**Find the sum of the series S8 for the series 10 – 5 + 2.5 – 1.25 + . . .**

**Answer:**

lets say -5=a1 2.5=a2 -1.25=a3

then series is :

a1 + ((a1)^2)/10) + ((a1)^3)/10^2) + …

it can be written as:

a1 (1 + ((a1)/10) + ((a1)^2/10^2) +…

then

a1 (1 + (a1/10) + (a1/10)^2 + …

now we can apply the summation formula which is

Sn = ( (1 - (r^n)) / (1 - r) ) x a1

for this series r=a1/10 , a1=-5 and n=7 (because there is one element outside which is 10)

then

S7 = -3.36

S8 = 10 + (-3.36) = 6.64