Question

$p,q,r,s$ and $t$ are in A.P. and are equal. If $q+r+s=15$ and $\frac{1}{q}+\frac{1}{r}+\frac{1}{s}=\frac{3}{5},$ which is G.M. of $p$ and $t$ ?

• A. $3$
• B. $5$
• C. $9$
• D. None of these

Answer 1

The correct option is B $5$

Given $p,q,r,s$ and $t$ are in AP.
$⟹q-p=r-q=s-r=t-s⟹2q=r+p,2r=s+q$ and $2s=t+r$

Given $q+r+s=15$ and $2r=s+q$,

$r+2r=s+q+r⟹3r=15⟹r=5$ [adding r on both sides]

So, we now have $p=q=r=s=t=5$.

GM of $p$ and $t=\sqrt{p\ast t}=\sqrt{5\ast 5}=5$.