Question

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

. It follows a times 10 pattern: 4, 40, 400, 4000, ….

Answer 1

The sequence is geometric.

`\texttt{Recursive formula, }t_n=10t_(n-1)`

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)`