Explanation:
The sum of an infinite geometric series is expressed according to the formula;
a 1 r where;
a is the first term of the series
r is the common ratio
If the sum of an infinite geometric series is three times the first term, this is expressed as
S∞ = 3a
Substitute S = 3a into the formula above to get the common ratio r;
a
3a 1-r
cross multiply
3a(1-r) = a
3(1-r) = 1
open the parenthesis
3- 3r 1
subtract 3 from both sides
33r31-3
-3r = -2
2|3 r =
Hence the common ratio of this series is 2 upon 3
= 2\3