Figure 6 Write the first five terms of the sequence defined by the recursive formula. They already told us what A sub one and A sub zero is. Example 5: Writing the Terms of a Sequence Defined by a Recursive Formula Write the first five terms of the sequence defined by the recursive formula.
When the output gets too large for the calculator, it will not be able to calculate the factorial.
Their growth follows the Fibonacci sequence, a famous sequence in which each term can be found by adding the preceding two terms. They tell us that A sub two is going to be A sub two minus one, so that's A sub one.
It's going to be A sub two, three minus one is two, three minus two is one. Instead, we describe the sequence using a recursive formula, a formula that defines the terms of a sequence using previous terms.
And then finally A sub four, which I will do in a color that I'll use, I'll do it in yellow. The Fibonacci sequence cannot easily be written using an explicit formula.
Factorials get large very quickly—faster than even exponential functions! Is there a pattern for the Fibonacci sequence? So times A sub two, times A, and then a blue color. Other examples from the natural world that exhibit the Fibonacci sequence are the Calla Lily, which has just one petal, the Black-Eyed Susan with 13 petals, and different varieties of daisies that may have 21 or 34 petals.
After the first two terms, each term is the sum of the previous two terms.