Question

If a, b, c are in AP as well as in GP then

• A. a + b + c = 1
• B. a - b - c = -1
• C. a = b = c
• D. a x b x c = 1

Answer 1

The correct option is C a = b = c

Given,

$2b=a+c$ .......( 1 )... a, b, c are in A.P.

$b^2=ac$ .......( 2 )... a, b, c are in G.P.

From ( 1 ) and ( 2 )...

$\Rightarrow (\frac{a+c}{2}{)}^2=ac$

$\Rightarrow a^2+c^2+2ac=4ac$

$\Rightarrow a^2-2ac+c^2=0$

$\Rightarrow (a-c{)}^2=0$

$\therefore a=c$

From ( 1 )...

$b=\frac{a+a}{2}=a$

$\therefore a=b=c$ (Ans $\to$ C)