Geometric Sequence: Find X, 5th Term

[alijan kk]

Homework Statement

The first three terms of a GP are X,X+2,X+3. The value of X and the fifth term is.[/B]
(a)-4,1/4
(b)4,1/4
(c)2,1/4
(d)-2,-1/4

Homework Equations

The Attempt at a Solution

(x+2/x)=(x+3)/(x+2)
(x+2)²=x²+3x
x²+2x+4=x²+3x
x=4

so i think r=(x+2)/x
putting x=4
r=3/2

also r=(x+3)/(x+2)
putting x=4
r=7/6

why the common ratio is different if it is a G.P ?

 

[PeroK]

If $x = 4$, write out the sequence and see what you get.

 

[alijan kk]

If $x = 4$, write out the sequence and see what you get.

the new sequence would be

4,6,7

it is not a geometric sequence and how can be the fifth term be less than one ?

 

[PeroK]

the new sequence would be

4,6,7

it is not a geometric sequence and how can be the fifth term be less than one ?

Exactly. It's not a geometric sequence. Maybe you made a mistake somewhere calculating $x$.

 

[alijan kk]

Exactly. It's not a geometric sequence. Maybe you made a mistake somewhere calculating $x$.

no I have done it many times. Is there any mistake in the question. ?

 

[PeroK]

no I have done it many times. Is there any mistake in the question. ?

Try doing, $(x +2)^2$ carefully.

 

[alijan kk]

Try doing, $(x +2)^2$ carefully.

ohhhh
than x= -4
and the sequence

-4 -2 -1 -1/2 -1/4

and the fifth term is -1/4

so the ans should be
-4 and -1/4