Question

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.

Answer 1

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

Answer 2

Thanks a lot:)