Problem

Write an explicit formula that represents the sequence defined by the following recursive formula:
\[
a_{1}=96 \text { and } a_{n}=-\frac{1}{4} a_{n-1}
\]
Answer: \( a_{n}= \)
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Answer

\(a_{n} = 96(-\frac{1}{4})^{n-1}\)

Steps

Step 1 ：\(a_{1} = 96\)

Step 2 ：\(a_{n} = -\frac{1}{4} \cdot a_{n-1}\)

Step 3 ：\(a_{n} = 96(-\frac{1}{4})^{n-1}\)

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