Question

What is the sum of the first 5 terms of a geometric series with a sub 1 = 10 and r = 1/5?

Answer 1

12.496

Explanation:

a=10 (first term)

r= 1/5 (common ratio)

sum of first five terms

`s_(5) = \frac{a( 1 - {r}^(n) ) }{1- r}`

=10{1-⅕⁵} ÷ 1-⅕

=10{1 - 1/3125} ÷ 4/5

=10{3124/3125} ÷ 4/5

=9.9968÷0.8

=12.496.

OR

a+ar+ar²+ar³+ar⁴

=10+(10x⅕)+(10x⅕²)+(10x⅕³)+(10x⅕⁴)

=10+2+0.4+0.08+0.016

=12+0.48+0.016

=12.496