If 5th and 8th terms of a G.P. be 48 and 384 respectively. find the G.P.

If 5th and 8th term of a G.P be 48 and 384 Respectively find the G.P

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To find the common ratio (r) of the geometric progression (G.P.), we can use the formula:

r = (8th term) / (5th term)

Given that the 8th term is 384 and the 5th term is 48, we plug these values into the formula:

r = 384 / 48
r = 8

Now we know that the common ratio (r) is 8.

To find the first term (a) of the G.P., we can use the formula:

a = (5th term) / (r^4)

Plugging in the values, we have:

a = 48 / (8^4)
a = 48 / 4096
a = 0.01171875

So the first term (a) of the G.P. is approximately 0.0117.

Finally, to find the G.P., we can use the formula:

G.P. = a, ar, ar^2, ar^3, ...

Substituting the values we found, we have:

G.P. = 0.0117, 0.09375, 0.75, 6, 48, ...

Therefore, the G.P. is 0.0117, 0.09375, 0.75, 6, 48, ...

To find the common ratio and the first term of a geometric progression (G.P.), we need to use the given information about the 5th and 8th terms.

Let's assume that the first term of the G.P. is 'a' and the common ratio is 'r'. We can form two equations using the given information.

The 5th term of the G.P. is given as 48, so:
a * r^4 = 48 (Equation 1)

The 8th term of the G.P. is given as 384, so:
a * r^7 = 384 (Equation 2)

To solve these equations, we can divide Equation 2 by Equation 1 to eliminate 'a':
(r^7) / (r^4) = 384 / 48
r^3 = 8
Taking the cube root of both sides:
r = 2

Now that we have the value of the common ratio (r = 2), we can substitute it into either Equation 1 or Equation 2 to find the first term 'a'.

Let's use Equation 1:
a * (2^4) = 48
16a = 48
a = 48 / 16
a = 3

Therefore, the G.P. is 3, 6, 12, 24, 48, ...

So, the common ratio is 2, and the first term is 3.