For what values of x, the numbers are in G.P?
The given numbers are − 2 7 , x , − 7 2 .
Let the common ratio of the first two terms and last two terms of the G.P. be r 1 , r 2 respectively.
The common ratio of the first two terms is given by,
r 1 = x − 2 7 = − 7 x 2 (1)
The common ratio of the last two terms is given by,
r 2 = − 7 2 x = − 7 2 x (2)
If all the terms are in G.P., then
r 1 = r 2
Substitute the values of r 1 , r 2 from equation (1) and equation (2) in the above expression.
− 7 x 2 = − 7 2 x x 2 = − 2 × 7 − 2 × 7 = 1 x = 1
Further simplify the above equation.
x = ± 1 .
Thus, for x = ± 1 , the given numbers are in G.P.
The given numbers are
Let the common ratio of the first two terms and last two terms of the G.P. be
The common ratio of the first two terms is given by,
The common ratio of the last two terms is given by,
If all the terms are in G.P., then
Substitute the values of
Further simplify the above equation.
Thus, for
