Question

Insert three number between 1 and 256 so that the resulting sequence is GP​

Answer 1

Answer:

4,16 and 64

Step-by-step explanation:

It will result as GP series

Answer 2

$\textbf{\underline{\underline{According\:to\:the\:Question}}}$

Assumption

Required Numbers

1 , Y1 , Y2 , Y3 , 256

These are in GP

Now,

Assume r be the common ratio

Using Formula

${\boxed{\bigstar{{a_{n}=ar^{n-1}}}}}$

$\tt{\rightarrow a_{5}=81}$

$\tt{\rightarrow ar^{5-1}=256}$

Here,

a = 1

$\tt{\rightarrow 1\times r^4=256}$

$\tt{\rightarrow r^4=256}$

r = ±4

Hence,

r = 4

Y1 = r = 4

Y2 = r² = 16

Y3 = r³ = 64

Also,

r = -4

Y1 = r = -4

Y2 = r² = 16

Y3 = r³ = -64