The third term of a geometric progression is 9 and the fifth term is 16. find the 4th term

Answer 1

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.