Question

If 4, x, y, 108 are the consecutive terms of a G.P., find x and y.

Answer 1

Given:

4, x, y, 108 are the consecutive terms of a G.P.

To find:

The x and y.

Solution:

The nth term of a G.P. is:

$a_n=ar^{n-1}$

Where, a is the first term and r is the common ratio.

Let us consider 4, x, y, 108 are the first 4 terms of the G.P. Here 4 is the first term of the given G.P.

Suppose r  the common ratio, then 4th term of the given G.P. is:

$a_4=4(r)^{4-1}$

$a_4=4(r)^{3}$

The 4th term of the G.P. is 108.

$4(r)^{3}=108$

$r^{3}=\dfrac{108}{4}$

$r^{3}=27$

$r^{3}=3^3$

On comparing both sides, we get

$r=3$

The common ratio is 3.

The second term of the given G.P. is:

$x=4r$

$x=4(3)$

$x=12$

The third term of the given G.P. is:

$y=xr$

$y=12(3)$

$y=36$

Therefore, the value x is 12 and the value of y is 36.