<PRE><B>Question 193885</B>
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</PRE>