Question

If a,b,c,d are in G.P., then ${(a+b)}^2$, ${(b+c)}^2$, ${(c+d)}^2$ are in:

• A. A.P.
• B. G.P.
• C. H.P.
• D. None

Answer 1

The correct option is B

G.P.

b=ar, c=a $r^2$, d=a $r^3$

Then ${(a+b)}^2$ = $a^2$ ${(1+r)}^2$, $a^2$ $r^2$(1+ $r^2$),

${(c+d)}^2$ = $a^2$ $r^4$ ${(1+r)}^2$

⇒ ${(a+b)}^2$, ${(b+c)}^2$, ${(c+d)}^2$ are in G.P.