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Use the initial term and the recursive formula to find an explicit formula for the sequence . Write your answer in simplest form. a = ______
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Q. Use the initial term and the recursive formula to find an explicit formula for the sequence . Write your answer in simplest form. a = ______
- Start with Initial Term: The initial term of the sequence is given as . This is the starting point of our sequence.
- Define Recursive Formula: The recursive formula given is , which means each term is less than the previous term. However, this recursive formula is not properly defined. A recursive formula should relate the term to . Let's assume the correct recursive formula is , where represents the position in the sequence.
- Find Explicit Formula: To find the explicit formula, we need to express the nth term in terms of the initial term and . Since the sequence decreases by each time, we can write the explicit formula as , where is the first term of the sequence.
- Substitute Initial Term: Substitute the initial term into the explicit formula to get .
- Simplify Explicit Formula: Simplify the explicit formula by distributing the across the term: .
- Combine Like Terms: Combine like terms to get the final explicit formula: .
