Question

Insert three numbers $1$ and $256$ so that the resulting sequence is a G.P.

• A. $0,16,64$
• B. $4,0,64$
• C. $4,6,64$
• D. $4,16,64$

Answer 1

The correct option is D $4,16,64$

Let, $g_1,g_2,g_3$ be three numbers between $1$ and $256$

$1,g_1,g_2,g_3,256$ are in $G.P$

First term $a=1$

$5^{th}$ term $=256$

$⟹a{r}^4=256$

$⟹\left(1\right)r^4=256$

$⟹r^4=4^4$

$\therefore r=4$

Now, $g_1=ar=1\times 4=4$

$g_2=a{r}^2=1\times 4^2=16$

$g_3=a{r}^3=1\times 4^3=64$

The required numbers are $4,16,64$