Question
\( \begin{array}{l}\text { 40) Write a recursive formula for the explicit formula. } \\ a_{n}=-7 n+52 \\ a_{1}= \\ \ a_{n}= \end{array} \)
Ask by Ramos Greene. in the United States
Mar 14,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The recursive formula is:
\[
a_1 = 45,\quad a_{n+1} = a_n - 7.
\]
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Bonus Knowledge
To derive a recursive formula from the explicit formula \( a_n = -7n + 52 \), we can first find the initial term and the relationship between consecutive terms. For \( a_1 \), substitute \( n = 1 \): \( a_1 = -7(1) + 52 = 45 \). Now, to obtain the recursive relation, we can compute the difference between terms: \[ a_n = a_{n-1} - 7 \] Therefore, the recursive formula is: \( a_1 = 45 \) \( a_n = a_{n-1} - 7 \) for \( n > 1 \).