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)=(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.