Question

lf $f\left(x\right)=lx$ and $a,b,c$ are in A.P. $k,l$ are constants. Then $f(a-k),f(b-k)$, and $f(c-k)$ are in

• A. A.P
• B. G.P
• C. H.P
• D. A.G.P

Answer 1

The correct option is A A.P

$f\left(x\right)=lx$
$f(a-k)=l(a-k)$ $a=K+\frac{f(a-k)}{l}$
$f(b-k)=l(b-k)$ $b=k+\frac{f(b-k)}{l}$
$f(c-k)=l(c-k)$ $c=k+\frac{f(c-k)}{l}$
$\because a,b,c$ are in A.P
$\therefore 2b=a+c$
$2(k+\frac{f(b-k)}{l})=k+\frac{f(a-k)}{l}+k+\frac{f(c-k)}{l}$
$2f(b-k)=f(a-k)+f(c-k)$
So, $f(a-k),f(b-k),f(c-k)$ are also in A.P.