If three positive numbers are inserted between 4 and 512 such tha… - Vidyadip

MCQ

If three positive numbers are inserted between $4$ and $512$ such that the resulting sequence is a $G.P.,$ which of the following is not among the numbers inserted?

A
$256$
B
$16$
C
$64$
✓
$128$

✓

Answer

Correct option: D.

$128$

Let $G.P.$ be $4, \mathrm{G}_1, \mathrm{G}_2, \mathrm{G}_3, 512$.
$ \Rightarrow a=4$ and $a_5=a \times r^4=512 \times 4 \times r^4=512$
$\Rightarrow r^4 $
$ =\frac{512}{4}=128$
$\Rightarrow r=4$
$ \mathrm{G}_1=\mathrm{a}_2=\mathrm{a} \times \mathrm{r}=4 \times 4=16 $
$ \mathrm{G}_2=\mathrm{G}_1 \times \mathrm{r}=16 \times 4=64 $
$ \mathrm{G}_3=\mathrm{G}_2 \times \mathrm{r}=64 \times 4=256$

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