The third term of a geometric progression is 9 and the fifth term is 16. find the 4th term
Let the first term be a and the common ratio be r.
We know that the third term is given by ar^2 = 9, and the fifth term is given by ar^4 = 16.
Dividing the two equations, we get (ar^4)/(ar^2) = 16/9.
Simplifying, we get r^2 = 16/9.
Taking the square root of both sides, we get r = +/- (4/3).
Since a * r^2 = 9, we can substitute r into the equation and solve for a:
a * (4/3)^2 = 9
a * 16/9 = 9
16a = 81
a = 81/16
Therefore, the first term is a = 81/16 and the common ratio is r = 4/3.
The fourth term is given by ar^3:
(81/16) * (4/3)^3 = 81/16 * 64/27 = 64/9.
So, the fourth term is 64/9.
To find the fourth term of a geometric progression, we need to know the common ratio between the terms. Given that the third term is 9 and the fifth term is 16, we can find the common ratio by dividing the fifth term by the third term.
Common ratio = fifth term / third term = 16 / 9
Now, we can find the fourth term by multiplying the third term by the common ratio.
Fourth term = third term * common ratio = 9 * (16 / 9)
Simplifying,
Fourth term = 16
Therefore, the fourth term of the geometric progression is 16.