Question

Given that the sum to infinity of a G.P. is 10. If the first term of the series is given as 5, determine the 3rd term.

Answer 1

a₃ = 1.25

Explanation:

the sum to infinity is calculated as

S ∞ =
`(a_(1) )/(1-r)`

a₁ is the first term and r the common ratio

given a₁ = 5 and S∞ = 10 , then

10 =
`(5)/(1-r)` ( multiply both sides by (1 - r)

10(1 - r) = 5

10 - 10r = 5 ( subtract 10 from both sides )

- 10r = - 5 ( divide both sides by - 10 )

r = 0.5

then

a₂ = a₁ × r = 5 × 0.5 = 2.5

a₃ = a₂ × r = 2.5 × 0.5 = 1.25