# Geometric Sequence

## 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

## 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
Homework Helper
Gold Member
2021 Award
If ##x = 4##, write out the sequence and see what you get.

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
Homework Helper
Gold Member
2021 Award
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##.

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
Homework Helper
Gold Member
2021 Award
no I have done it many times. Is there any mistake in the question. ?

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

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

PeroK