Use the initial term and the recursive formula to find an explicit formula for the sequence an. Write your answer in simplest form.a1=−47an=an−1−7an=_
Q. Use the initial term and the recursive formula to find an explicit formula for the sequence an. Write your answer in simplest form.a1=−47an=an−1−7an=_
Initialize Term and Recursive Formula: The initial term is a1=−47. The recursive formula is an=an−1−7. To find the explicit formula, we need to express an in terms of n.
First Few Terms Analysis: Let's look at the first few terms to see the pattern. a1=−47, a2=a1−7=−47−7=−54, a3=a2−7=−54−7=−61.
Identify Arithmetic Sequence Pattern: We notice that each term is 7 less than the previous term, which means the sequence is arithmetic with a common difference of −7.
Explicit Formula for Arithmetic Sequence: The explicit formula for an arithmetic sequence is an=a1+(n−1)d, where d is the common difference.
Substitute Values into Formula: Substitute a1=−47 and d=−7 into the formula: an=−47+(n−1)(−7).
Simplify Formula: Simplify the formula: an=−47−7n+7.
Combine Like Terms: Combine like terms: an=−7n−40.
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