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 :
Substitute
Step 2. Compute the difference between consecutive terms:
The recursive formula is of the form
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
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
.