Answer :
Answer:
The sequence is geometric.
[tex]\texttt{Recursive formula, }t_n=10t_{n-1}[/tex]
Step-by-step explanation:
If the sequence is arithmetic common difference will be same, if the sequence is arithmetic common ratio will be same.
Here the sequence is 4, 40, 400, 4000, …
Difference between terms
40 -4 = 36
400 - 40 = 360
They are not same , so the sequence is not arithmetic.
Ratio between terms
40/4 = 10
400/40 = 10
4000/400 = 10
They are same , so the sequence is geometric.
Now we need to find recursive formula for the sequence.
Recursive formula for GP
[tex]t_n=rt_{n-1}[/tex]
[tex]\texttt{Recursive formula, }t_n=10t_{n-1}[/tex]