Question

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

Answer 1

Answer:

The  recursive formula for the given sequence

                 $t_{n}= (2)^{n+2}$

Step-by-step explanation:

Explanation:-

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

First term is   a = 8

common ratio   $r = \frac{16}{8} =2$

                       $r = \frac{32}{16} =2$

                      $r = \frac{64}{32} =2$   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 ....