The second term of a Geometric Progression (G.P) is 9. If the fourth term is 81, find the common ratio.
Geometric Progression (G.P)
Terms of an infinite G.P. can be written as a, ar, ar2, ar3, ……arn-1
Where a is the first term and r is the common ratio.
The nth term (an) is calculated as arn-1
Common ratio =
an = arn-1
Second term = 9
n = 2
ar2-1 = 9
ar = 9 ------ eqn 1
Fourth term = 81
n = 4
ar4-1 = 81
ar3 = 81 ----- eqn 2
Get rid of a by dividing ----- eqn 2 by ----- eqn 1
=
Notes:
1. The a cancel each other
2. From law of indices am ÷ an = = am - n
3. r = r1
r3 - 1 = 9
r2 = 9
9 = 3 x 3 = 32
r2 = 32
Since the powers are the same, the bases are also the same.
r = 3
∴ common ratio = 3
