SOLUTION: the second term of the infinite geometric series, a + ar + ar^2 + ar^3...... is eaqual to 4 and the same to infinity of this series is 18. Find the two possible values of th

Click here to see ALL problems on Sequences-and-series

Question 193885: the second term of the infinite geometric series,
a + ar + ar^2 + ar^3......
is eaqual to 4 and the same to infinity of this series is 18. Find the two possible values of the common ratio, r. what are the corresponding values of a?
Found 2 solutions by radikrr, stanbon:
Answer by radikrr(7) (Show Source):
You can put this solution on YOUR website!
ar=4 a/(1-r)=18
a=4/r 4/r=(1-r)18
4/r=(1-r)18
2/9=(1-r)r
r^2-r+2/9=0
D = 1-8/9=1/9
r1=2/3 r2=1/3
a1=6 a2=18

Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
the second term of the infinite geometric series,
a + ar + ar^2 + ar^3......
is equal to 4 and the same to infinity of this series is 18. Find the two possible values of the common ratio, r. what are the corresponding values of a?
----------------
2nd term: a(2) = ar = 4
Sum : a/(1-r) = 18
--------------------------
Rearrange:
a = 4/r
---
Substitute:
(4/r)/(1-r) = 18
4/r = 18 - 18r
4 = 18r-18r^2
18r^2 - 18r +4 = 0
9r^2 - 9r + 2 = 0
9r^2 - 6r - 3r + 2 = 0
3r(3r-2)-(3r-2) = 0
(3r-2)(3r-1) = 0
r = 2/3 or r = 1/3
-------------
Since a = 4/r
a = 6 when r = 2/3 or a = 12 when r = 1/3
---------------------
Cheers,
Stan H