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Write an explicit formula for , the term of the sequence Answer:
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Q. Write an explicit formula for , the term of the sequence Answer:
- Identify Sequence Type: Identify whether the given sequence is geometric or arithmetic. The sequence has a common ratio between consecutive terms, as each term is obtained by multiplying the previous term by a constant. To find this constant, we can divide the second term by the first term: . Similarly, dividing the third term by the second term gives . Since the ratio is consistent, the sequence is geometric.
- Use Explicit Formula: Use the explicit formula for a geometric sequence, , where is the first term and is the common ratio. For the sequence , the first term, , is and the common ratio, , is .
- Substitute Values: Substitute the values of and into the formula to write an expression to describe the sequence. The expression for the sequence is a_n = 24 imes (- rac{1}{2})^{(n-1)}.
