Question

what is the sum of the first five ferms of a geometric series with a1=10 and r=1/5? express your answer as an important fraction in lowest terms without using spaces

Answer 1

The sum of any geometric sequence, (technically any finite set is a sequence, series are infinite) can be expressed as:

s(n)=a(1-r^n)/(1-r), a=initial term, r=common ratio, n=term number

Here you are given a=10 and r=1/5 so your equation is:

s(n)=10(1-(1/5)^n)/(1-1/5) let's simplify this a bit:

s(n)=10(1-(1/5)^n)/(4/5)

s(n)=12.5(1-(1/5)^n) so the sum of the first 5 terms is:

s(5)=12.5(1-(1/5)^5)

s(5)=12.496

as an improper fraction:

(125/10)(3124/3125)

390500/31240

1775/142