How do I find out the sum of a infinite geometric sequence ?

Question

the sequence

20,-40/3,80/9, -160/27,320/81,

Answer 1

20 + (-40/3) + 80/9 + (-160/27) + ... is a geometric series with first term a = 20 and common ratio r = -2/3.

Since -1 < r < 1, the series has a finite sum given by the formula: a / (1-r)

So, the sum of the series is 20 / [1 - (-2/3)] = 20 / (5/3) = 12