Respuesta :
Answer:
The recursive formula for the given sequence
[tex]t_{n}= (2)^{n+2}[/tex]
Step-by-step explanation:
Explanation:-
Given sequence is 8 , 16, 32, 64 ,.....
First term is a = 8
common ratio [tex]r = \frac{16}{8} =2[/tex]
[tex]r = \frac{32}{16} =2[/tex]
[tex]r = \frac{64}{32} =2[/tex] and so on..
Given sequence of the common ratio 'r' is equal
The [tex]n^{th}[/tex] term of the sequence
[tex]t_{n} = a r^{n-1}[/tex]
[tex]t_{n}= 8 (2)^{n-1}[/tex]
[tex]t_{n}= (2)^{(3+n-1)}[/tex]
[tex]t_{n}= (2)^{n+2}[/tex]
This is recursive formula for the given sequence
[tex]t_{n}= (2)^{n+2}[/tex]
Verification:-
[tex]t_{n}= (2)^{n+2}[/tex]
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 ....
