Question

If $a,b,c$ are in A.P, $b,c,d$ are in G.P and $c,d,e$ are in H.P. then find the value of $\mid c\mid$, given that $a=32$ and $e=2$.

• A. $7$
• B. $8$
• C. $9$
• D. $10$

Answer 1

Answer: (B)

$8$

Given a,b,c are in A.P, b,c,d are in G.P and c,d,e are in H.P,

$\therefore 2b=a+c,c^2=bdandd=\frac{2ce}{c+e}$

$\therefore c^2=\left(\frac{a+c}{2}\right)\left(\frac{2ce}{c+e}\right)$

$\Rightarrow 2c(c+2)=2\left(2\right)(32+c)$ ....... $e=2$

$\Rightarrow c^2=64$

$\therefore \mid c\mid =8$