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

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Answer

Substitute the given values: a_n = 96 * (-\frac{1}{4})^{n-1}

Steps

Step 1 ：Find the common ratio, r: r = -\frac{1}{4}

Step 2 ：Use the formula for an explicit sequence: a_n = a_1 * r^{n-1}

Step 3 ：Substitute the given values: a_n = 96 * (-\frac{1}{4})^{n-1}