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:
[tex]a_n=ar^{n-1}[/tex]
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:
[tex]a_4=4(r)^{4-1}[/tex]
[tex]a_4=4(r)^{3}[/tex]
The 4th term of the G.P. is 108.
[tex]4(r)^{3}=108[/tex]
[tex]r^{3}=\dfrac{108}{4}[/tex]
[tex]r^{3}=27[/tex]
[tex]r^{3}=3^3[/tex]
On comparing both sides, we get
[tex]r=3[/tex]
The common ratio is 3.
The second term of the given G.P. is:
[tex]x=4r[/tex]
[tex]x=4(3)[/tex]
[tex]x=12[/tex]
The third term of the given G.P. is:
[tex]y=xr[/tex]
[tex]y=12(3)[/tex]
[tex]y=36[/tex]
Therefore, the value x is 12 and the value of y is 36.
