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

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