![]() ![]() This work is licensed under a Creative Commons Attribution 4.0 License. The recursive formula calculates the next term of a geometric sequence, n+1, n + 1, based on the previous term, n. 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. We can divide any term in the sequence by the previous term. A recursive formula allows us to find any term of a geometric sequence by using the previous term. Then he explores equivalent forms the explicit formula and finds the corresponding recursive formula. Using Recursive Formulas for Geometric Sequences. 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? Explicit & recursive formulas for geometric sequences Google Classroom About Transcript Sal finds an explicit formula of a geometric sequence given the first few terms of the sequences. The sequence of data points follows an exponential pattern. Substitute the common ratio into the recursive formula for geometric sequences and define. To obtain the third sequence, we take the second term and multiply it by the common ratio. Then we multiply the first term by a fixed nonzero number to get the second term of the geometric sequence. ![]() To generate a geometric sequence, we start by writing the first term. Then, determine an explicit formula for the general term. How to Derive the Geometric Sequence Formula. Determine whether the following sequence is arithmetic, geometric, or neither. The common ratio can be found by dividing the second term by the first term. Use the recursive formula for a geometric sequence to find the first five terms of a geometric sequence with a starting term of 5 and a common ratio of 7. Write a recursive formula for the following geometric sequence. ![]()
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