First slide

Geometric progression

Question

If the pth, qth and rth terms of an A.P. are in G.P., then the common ratio of the G.P. is

Moderate

A

$\frac{pr}{q^{2}}$
B

$\frac{r}{p}$
C

$\frac{q + r}{p + q}$
D

$\frac{q - r}{p - q}$

Solution

pth, qth, rth terms of A.P. are
$a + (p - 1) d = x$ ………..(i)
$a + (q - 1) d = xR$ ……..(ii)
$a + (r - 1) d = {xR}^{2}$ …….(iii)
where R is common ratio of G.P.
Subtracting (2) from (3) and (1) from (2) and then dividing
the former by the later, we have
$\frac{q - r}{p - q} = \frac{{xR}^{2} - xR}{xR - x} = R$

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