Question

If the P^th, q^th , and r^th tems of an A.P. are in G.P., then common ratio of the G.P. is

• A.
• B.
• C.
• D.

Answer 1

The correct option is D

$p^{th},q^{th},r^{th}$ terms of A.P. are

$a+(p-1)d=x$

$a+(q-1)d=xR$

$a+(r-1)d=x{R}^2$
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 $R=\frac{q-r}{p-q}$