Question

the sum of an infinite geometric series is 20, and the common ratio is 0.2. Find the first term of this series

Answer 1

a₁ = 16

Explanation:

The sum to infinity of a geometric series is

S ∞ =
`(a_(1) )/(1-r)`

where a₁ is the first term and r the common ratio , then

`(a_(1) )/(1-0.2)` = 20

`(a_(1) )/(0.8)` = 20 ( multiply both sides by 0.8 to clear the fraction )

a₁ = 0.8 × 20 = 16