# How do you write a recursive rule for a sequence

### Recursive rules with sequences worksheet answers

While we have seen recursive formulas for arithmetic sequences and geometric sequences, there are also recursive forms for sequences that do not fall into either of these categories. Instead, we describe the sequence using a recursive formula, a formula that defines the terms of a sequence using previous terms. Is there a recursive formula for the Fibonacci sequence? It may be the case with geometric sequences that the graph will increase or decrease. The numbers in the sequence are 1, 1, 2, 3, 5, 8, 13, 21, 34,…. When the output gets too large for the calculator, it will not be able to calculate the factorial. Create a recursive formula by stating the first term, and then stating the formula to be the common ratio times the previous term. Find the common ratio. The common ratio is usually easily seen, which is then used to quickly create the recursive formula. For calculator. After the first two terms, each term is the sum of the previous two terms. To find the third term, substitute the initial term and the second term into the formula.

The Fibonacci sequence cannot easily be written using an explicit formula. After the first two terms, each term is the sum of the previous two terms. Each term of the Fibonacci sequence depends on the terms that come before it.

The number you multiply or divide.

This means the quotient gets smaller and, as the plot of the terms shows, the terms are decreasing and nearing zero.

This is the first term.

Find the common ratio. Factorials get large very quickly—faster than even exponential functions!

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