Question

Find three geometric means between 1 and 16$a^4$.

• A. 2a, 4$a^2$, 8$a^3$
• B. 2a,4a,8a
• C. 2a, 2$a^2$, 2$a^3$
• D. None of the above

Answer 1

The correct option is A 2a, 4$a^2$, 8$a^3$

Let the required geometric means be G1,G2 and G3.
Then 1, G1,G2 , G3 and 16$a^4$ are in G.P.
$\therefore$ Fifth term = 16$a^4$ = 1 x $r^4$
$r^4$ = 16$a^4$ i.e. r = 2a
$\therefore$ G1 = 1 x r = 1 x 2a = 2a
G2 = 1 x $r^2$ = 1 x 4$a^2$ = 4$a^2$
G3 = 1 x $r^3$ = 1 x 8$a^3$ = 8$a^3$