If 5th and 8th terms of a gp be 48 and 384 respectively find the gp if term of gp are real number

3, 6, 12, 24 ......

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the 5th and 8th terms are 3 terms apart, so r^3 = 384/48 = 8

so, r = 2

Now you know that the terms from 5 through 8 are
..., 48, 96, 192, 384, ...

It should be easy work to find where it starts, now.

If 5th and 8th term of a g.p be 48and 384 respectively. Find the g.p if termof g.p are real number.

To find the geometric progression (GP), we need to determine the common ratio (r) and the first term (a).

We are given that the 5th term of the GP is 48 and the 8th term is 384.

The nth term of a GP is given by the formula:
an = a * r^(n-1)

Using this formula, we can set up two equations to solve for r and a.

Equation 1:
48 = a * r^(5-1)

Equation 2:
384 = a * r^(8-1)

Dividing Equation 2 by Equation 1, we get:
(384/48) = (a * r^(8-1)) / (a * r^(5-1))

Simplifying the equation, we have:
8 = r^3

Taking the cube root of both sides, we find:
r = 2

Now that we know the value of r, we can substitute it into either equation to solve for a:

Using Equation 1:
48 = a * (2)^(5-1)

Simplifying, we have:
48 = a * 16

Dividing both sides by 16, we find:
a = 3

Therefore, the GP is: 3, 6, 12, 24, 48, 96, 192, 384,...

In general, to find the common ratio and first term of a geometric progression given certain terms, we can set up two equations using the formula for the nth term of the GP and solve for the unknown values.