Question

Ask by Ramos Greene. in the United States
Mar 14,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

The recursive formula is:

Solution

We start with the explicit formula
Step 1. Find the first term:
Substitute :
Step 2. Compute the difference between consecutive terms:
The recursive formula is of the form
To find the common difference , compute
Subtract :
Thus, the common difference is
Step 3. Write the recursive formula:
The recursive formula is

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Bonus Knowledge

To derive a recursive formula from the explicit formula , we can first find the initial term and the relationship between consecutive terms. For , substitute : . Now, to obtain the recursive relation, we can compute the difference between terms:
Therefore, the recursive formula is:

for .

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