The first term of an infinite geometric sequence is 2. The sum of the sequence is 6. What is the common ratio of the sequence?
The "formula" for the sum of an infinite sequence is given by
S = a0 / (1 - r)....where S is the sum, a0 is the initial value, and r is the common ratio...so we have...
6 = 2 / (1 - r) mutiply both sides by 1-r
6(1 - r) = 2 simplify
6 - 6r = 2 rearrange
4 = 6r solve for r
r = 2/3