# Writing a recursive definition for a sequence

This right over here would be the second term. Well, we're defining what a sub 1 is. So it's going to be a sub 1 plus 3.

### Recursive definition calculator

We may see the sequence in the leaf or branch arrangement, the number of petals of a flower, or the pattern of the chambers in a nautilus shell. Well, we're defining what a sub 1 is. This right over here is a plus 3. Create a recursive formula by stating the first term, and then stating the formula to be the common ratio times the previous term. And I'm just going to add 3 for every successive term. You get to 7. But I'll do a again-- a sub k. Well, what about a sub 3? For the fourth term, we add 4 three times. Figure 8. You add 3.

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. When k is 1, we get 1. Well, they're saying, well, it's going to be a sub 2 minus 1. 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.

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