Problem: The sum to infinity of the terms of an infinite geometric progression is 6. The sum of the first two terms is 4/2. The first term of the progression is:
Answer Choices:
A. 3 or 121
B. 1
C. 221
D. 6
E. 9 or 3
Solution:
Let the first two terms be a and ar where −1<r<1
∴a(1+r)=421.
Since s=a/(1−r)=6,a=6(1−r)
∴6(1−r)(1+r)=421;∴r=±21;∴a=3 or 9