Question

If a,b,c are in GP,Which of the following will be the common ratio of the GP.

• A.
• B.
• C.
• D.

Answer 1

Answer: (A), (B), (C), (D)

The correct options are
A

B

C

D

If the common ratio is r,

b=ar

c=a$r^2$

$\Rightarrow$ $\frac{b}{a}$ = r, ----------(A)

$\frac{c}{a}$ = $r^2$

$\Rightarrow$ $(\frac{c}{a}{)}^{\frac{1}{2}}$ = r,--------------(B)

$\frac{c}{b}$ = $\frac{a{r}^2}{ar}$

$\Rightarrow$ $\frac{c}{b}$ = r, ----------(C)

$\frac{c-b}{b-a}=\frac{a{r}^2-ar}{ar-a}=\frac{r(ar-a)}{(ar-a)}$

= r -------------------------(D)