Question

the sum of an infinite geometric series is 6 and the sum of its first two terms is 9/2.find the first term and common ratio.​

Answer 1

Answer:

Let us assume the first term is a and common ratio is r.

For sum of infinite geometric progression, formula is -

S=a1−r

Where S = sum of infinite geometric progression

6=a1−r

⟹a=6(1−r)

⟹a=6−6r

Also, sum of first two terms =a+ar

⟹92=a+ar

Putting a=6−6r in above equation, we have

⟹92=6−6r+r(6−6r)=6(1−r2)

⟹3=4−4r2

⟹4r2=1

⟹r=±12

When r=12

⟹a=6−6×12=6−3=3

OR

When r=−12

⟹a=6+6×12=6+3=9

So, the first term is either 3 or 9.