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

User Kohske
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1 Answer

6 votes

Answer:

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 ....

User Omzer
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