The third term of a geometric progressiom is nine times the first term.if the second term is one-twenty fourth the fifth term.find the fourth term.ar^2=9a. r=sqr of 9 r=3.pls teach me how to get the first term and i can get the 4th term myself

To find the first term in a geometric progression, we can use the given information about the third term and the constant ratio.

Let's denote the first term as 'a' and the common ratio as 'r'. We are given that the third term is nine times the first term, so we have:

Third term = 9a

We also know that the common ratio 'r' can be found using the equation ar^2 = 9a. Simplifying this equation, we get:

r^2 = 9

Taking the square root of both sides, we find:

r = ±√9

Since a negative ratio doesn't make sense in this context, we take the positive square root and find:

r = 3

Now that we know the value of 'r', we can calculate the value of the first term 'a'. Substituting the value of 'r' into the equation ar^2 = 9a, we get:

a(3)^2 = 9a

9a = 9a

This equation holds true for any value of 'a'. Thus, the value of the first term 'a' can be any real number.

Now, to find the fourth term, we can use the formula for the nth term of a geometric progression:

nth term = a * r^(n-1)

Substituting 'a = any real number' and 'r = 3', and simplifying the equation where n = 4 (since we want the fourth term), we get:

Fourth term = a * 3^(4-1)

Fourth term = a * 3^3

Fourth term = a * 27

Therefore, the fourth term is 27a, where 'a' can be any real number.

a ar^1 ar^2 ar^3 .... ar^(n-1)

so
a r^2 = 9 a
a r^1 = (1/24)ar^4
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so
r = 3

a(3) = (1/24)a (3)^4
This is not possible. You have a typo.