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

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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.

User Barath Ravikumar
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