If the fifth term of a G.P. Is 81 and second term is 24, find the g.p. Sir this question answer 16,24,36,54 please help

You posted over 20 of these type of questions yesterday.

Did you even look at some of the replies?
Are you attempting to learn how to do these kind of problems?

Show me how you started this one, and I will try to guide you along.

Sir it is last question after that no post any question

ar^4 = 81

ar^2 = 24

r^3 = 81/24 = 27/8

clearly r = 3/2

You could have discovered that just by looking at the terms given.

To find the geometric progression (G.P.), we need to determine the common ratio (r) first.

In a G.P., the formula for finding any term is given by:

an = a1 * rn-1

where:
an = nth term
a1 = first term
r = common ratio
n = term number

Given that the second term (a2) is 24, and the fifth term (a5) is 81, we can use these values to set up two equations:

a2 = a1 * r
a5 = a1 * r^4

Plugging in the values:
24 = a1 * r
81 = a1 * r^4

Now, let's solve these two equations to find the values of a1 and r.

Divide the second equation by the first equation:

(81/24) = (a1 * r^4) / (a1 * r)
3.375 = r^3

Now, find the cube root of both sides:

∛(3.375) = ∛(r^3)
r = 1.5

Substituting the value of r into the first equation:

24 = a1 * 1.5
24 / 1.5 = a1
16 = a1

Now that we have found a1 and r, we can generate the G.P. sequence. The terms will be:

a1 = 16
a2 = 16 * 1.5 = 24
a3 = 24 * 1.5 = 36
a4 = 36 * 1.5 = 54

Hence, the G.P. sequence with the given conditions is 16, 24, 36, 54.