IN A GP THE 5TH AND 8TH IS 24 AND 72 FIND THE 6TERM

a ar ar^2 ar^3 etc

a r^n-1

a r^4 = 24
a r^7 = 72

r^7/r^4 = 72/24

r^3 = 3

r = 3^(1/3)

a 3^(4/3) = 24

a = 24 * 3^-(4/3)

a = 5.55
r = 1.44

check a r^4 = 24.01
a r^7 = 72.04 ok

5 .55

That is a

but you asked for term 6
which is

a r^5

5.55 * 1.44^5

about 34.4

To find the 6th term in a geometric progression (GP), we need to first determine the common ratio (r) of the sequence.

In a geometric progression, each term is obtained by multiplying the previous term by a constant value, which is the common ratio. Let's denote the first term as 'a' and the common ratio as 'r'.

Given that the 5th term is 24 and the 8th term is 72, we can set up the following equations:

a * r^4 = 24 ------ (1) (since the 5th term is a * r^4)
a * r^7 = 72 ------ (2) (since the 8th term is a * r^7)

To eliminate 'a', we can divide equation (2) by equation (1):

(a * r^7) / (a * r^4) = 72 / 24
r^3 = 3

Taking the cube root of both sides, we find:

r = ∛3

Now that we have the common ratio, we can find the 6th term using the formula:

Term(n) = a * r^(n-1)

Plugging in 'n = 6', 'a' as the first term, and 'r' as the common ratio, we get:

Term(6) = a * (∛3)^(6-1)

Simplifying:

Term(6) = a * (∛3)^5
= a * (3^(1/3))^5 [since ∛3 = (3^(1/3))]
= a * 3^(5/3)

We do not have the value of 'a' (the first term) in the given information. Without knowing the first term, we cannot calculate the 6th term.