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

Answer:

a₁ = 16

Step-by-step explanation:

The sum to infinity of a geometric series is

S ∞ = $\frac{a_{1} }{1-r}$

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

$\frac{a_{1} }{1-0.2}$ = 20

$\frac{a_{1} }{0.8}$ = 20 ( multiply both sides by 0.8 to clear the fraction )

a₁ = 0.8 × 20 = 16