Question

What is the sum of the infinite geometric series?

120 + 20+ 10/3 + 5/9+...

Answer 1

C. 144

Explanation:

Answer 2

for an infinite geometric series the formula for the sum of the infinite geometric series when the common ratio is less than one is given by

`(a_(1) )/(1 - r)` =
`(120)/(1 - (1)/(6) ) = (120)/((5)/(6) ) =`
`(120 * 6)/(5)` = 144.

Explanation:

i) from the given series we can see that the first term is
`a_(1 )` = 120.

ii) let the common ratio be r.

iii) the second term is 20 = 120 × r

therefore r = 20 ÷ 120 =
`(1)/(6)`

iv) the third term is
`(10)/(3)` = 20 × r

therefore r =
`(10)/(3)` ÷ 20 =
`(1)/(6)`

v) for an infinite geometric series the formula for the sum of the infinite geometric series when the common ratio is less than one is given by

`(a_(1) )/(1 - r)` =
`(120)/(1 - (1)/(6) ) = (120)/((5)/(6) ) =`
`(120 * 6)/(5)` = 144.