Given the first several terms of a geometric sequence, write its recursive formula. State the initial term. Find the common ratio by dividing any term by the preceding term. Substitute the common ratio into the recursive formula for a geometric sequence.

A recursive formula is a mathematical equation that defines a sequence by expressing each term in the sequence as a function of the preceding terms. These formulas are particularly useful in describing and analyzing patterns that emerge in sequences, such as geometric sequences.

A recursive formula is a mathematical expression that defines a sequence by relating each term in the sequence to the previous term(s). It provides a way to generate the terms of a sequence by applying a specific rule or pattern repeatedly.

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Recursive formulas define each term of a sequence using previous terms. Recursive formulas must state the initial term, or terms, of a sequence. A set of terms can be written by using a recursive formula.

When your pre-calculus teacher asks you to find any term in a recursive sequence, you use the given term (at least one term, usually the first, is given) and the given formula that allows you to find the other terms in the sequence.

Use the recursive formula to write a geometric sequence whose common ratio is an integer. Show the first four terms, and then find the 10 th term. Use the explicit formula to write a geometric sequence whose common ratio is a decimal number between 0 and 1.

Jan 1, 2025 · Recursion defines an entire sequence based on the first term and the pattern between consecutive terms. Recursive thinking involves describing patterns as a function of the previous term(s). a k = f ( a k − 1 )

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