A goemetric progression is such that the 3rd term is 9times the first term ,while the 2nd term is one-twenty fourth of the 5th term.Find the 4th term

ar^2=9a

ar^2/a=9a/a
r^2=9
r=√9
r=3 or -3

ar^2 = 9a

so, r = 3 or -3

24*ar = ar^4
24 = r^3
huh? I thought r^3 was 27.
I suspect a typo.

questions

Answer

To find the 4th term of the geometric progression, let's start by assigning variables to the terms. Let's call the first term "a" and the common ratio of the progression "r".

Given information:
The 3rd term is 9 times the first term:
Third term = 9a

The 2nd term is one-twenty fourth of the 5th term:
Second term = 1/24 * Fifth term = (1/24) * ar^4

Now, let's use the information provided to form equations:

Equation 1: Third term = 9 times the first term
9a = 9a

Equation 2: Second term = one-twenty fourth of the 5th term
(1/24) * ar^4 = (1/24) * ar^4

Since both equations simplify to 9a = 9a and (1/24) * ar^4 = (1/24) * ar^4, they do not provide any additional information to solve for the variables.

Therefore, with the given information, we cannot determine the values of "a" or "r". Consequently, we are unable to find the 4th term of the geometric progression without further information.