Question

Write a recursive formula for each sequence given or described below.

Answer 1

Answer:

The sequence is geometric.

$\texttt{Recursive formula, }t_n=10t_{n-1}$

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

                      $t_n=rt_{n-1}$

$\texttt{Recursive formula, }t_n=10t_{n-1}$