Functions 11: Series and Sequence 2
posted by lg on .
The sum of the first two terms of a geometric sequence is 3. The sum of the next two terms is 4/3. Find the first four terms of the sequence.

Let the four terms be a,b,c,d, and be the common ratio.
b=ar
c=ar²
d=ar³
a+b=a(1+r)=3
c+d=ar²(1+r)=4/3
(c+d)/(a+b) = r² = (4/3)/3=4/9
=>
r=√(4/9)=±2/3, assume 2/3
a+b=a(1+r)=a(1+2/3)=5a/3=3
=>
a=9/5
b=ar=6/5
c=ar²=4/5
d=ar³=8/15 
Thanks a lot:)