Question 1162194: An infinite geometric series has a sum of 180 and a common ratio of 2/3. What is the first term of the series?
a. 120
b. 540
c. 60
d. 270
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website!
If we are summing infinitely many geometric sequence terms, and r is between -1 and 1 (exclusive of both endpoints), then we use the formula
S = a/(1-r)
where,
a = first term
r = common ratio and -1 < r < 1 must be true
S = infinite sum
We are given
S = 180
r = 2/3
note that r = 2/3 = 0.667 satisfies -1 < r < 1. Otherwise, the formula S = a/(1-r) would not apply, and the series would diverge.
So,
S = a/(1-r)
S(1-r) = a
a = S(1-r)
a = 180(1-2/3)
a = 180(1/3)
a = 180/3
a = 60
The first term is 60
Answer: C. 60
The geometric sequence looks like
60, 40, 80/3, ...
Each new term is found by multiplying the last term by 2/3
|
|
|
