Question

Identify the recursive formula for the following sequence. 8, 16, 32, 64, ...

Answer 1

The recursive formula for the given sequence

`t_(n)= (2)^(n+2)`

Explanation:

Explanation:-

Given sequence is 8 , 16, 32, 64 ,.....

First term is a = 8

common ratio
`r = (16)/(8) =2`

`r = (32)/(16) =2`

`r = (64)/(32) =2` and so on..

Given sequence of the common ratio 'r' is equal

The
`n^(th)` term of the sequence

`t_(n) = a r^(n-1)`

`t_(n)= 8 (2)^(n-1)`

`t_(n)= (2)^((3+n-1))`

`t_(n)= (2)^(n+2)`

This is recursive formula for the given sequence

`t_(n)= (2)^(n+2)`

Verification:-

`t_(n)= (2)^(n+2)`

put n=1 ⇒ t₁ = 8

put n=2 ⇒ t₂ = 16

put n=3 ⇒ t₃ = 32

put n=4 ⇒ t₄= 64

and so on..

The sequence 8 ,16 , 32 , 64 ....