the third and fifth term of a geometric progression are 9/2 and 81/8 find the common ratio and first term
Let the first term of the geometric progression be a and the common ratio be r.
The third term of the geometric progression is given by ar^2 and the fifth term is given by ar^4.
Given that the third term is 9/2, we have:
ar^2 = 9/2
Given that the fifth term is 81/8, we have:
ar^4 = 81/8
Now we have two equations:
1) ar^2 = 9/2
2) ar^4 = 81/8
Dividing equation 2 by equation 1, we get:
r^2 = (81/8)/(9/2)
r^2 = 9/4
r = 3/2 or -3/2
Since the common ratio of a geometric progression cannot be negative, we have r = 3/2.
Now we can substitute r = 3/2 into equation 1:
a(3/2)^2 = 9/2
a(9/4) = 9/2
9a/4 = 9/2
a = 4/2
a = 2
Therefore, the common ratio of the geometric progression is 3/2 and the first term is 2.