This work is licensed under a Creative Commons Attribution 4.0 License. Then each term is nine times the previous term. For example, suppose the common ratio is 9. The recursive formula shows how to find the next term based on the previous term. Each term is the product of the common ratio and the previous term. Confusing the explicit and recursive formulas for a sequence The explicit formula shows how to find any term based on the relationships between the term number and the term itself. A recursive formula allows us to find any term of a geometric sequence by using the previous term. It is, however, most common to divide the second term by the first term because it is often the easiest method of finding the common ratio. Using Recursive Formulas for Geometric Sequences. We can divide any term in the sequence by the previous term. The common ratio is also the base of an exponential function as shown in Figure 2ĭo we have to divide the second term by the first term to find the common ratio? The sequence of data points follows an exponential pattern. Consider a situation in which the value of a car depreciates 10 per year. Identify a sequence as arithmetic, geometric, or neither. Write an explicit formula for a sequence, and use the formula to identify terms in the sequence. Substitute the common ratio into the recursive formula for geometric sequences and define. Write a recursive formula for a sequence, and use the formula to identify terms in the sequence. The common ratio can be found by dividing the second term by the first term. If the terms of a sequence differ by a constant, we say the sequence is arithmetic. If we want to multiply the instead, we would write For example, This page titled 2.2: Arithmetic and Geometric Sequences is shared under a CC BY-SA license and was authored, remixed, and/or curated by Oscar Levin. Write a recursive formula for the following geometric sequence. Use notation to rewrite the sums: Solution.
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