# Writing a recursive rule

If b of one is equal to negative seven, then we know that this right over here is negative seven, and now we can figure out that b of two is equal to negative seven plus 12 which is equal to five.

Find the common ratio. Figure 6 Write the first five terms of the sequence defined by the recursive formula.

### How to write a recursive formula for a geometric sequence

The numbers in the sequence are 1, 1, 2, 3, 5, 8, 13, 21, 34,…. To summarize the process of writing a recursive formula for a geometric sequence: 1. Recursive formulas must always state the initial term, or terms, of the sequence. In most geometric sequences, a recursive formula is easier to create than an explicit formula. You have to keep recursing backwards, so b of three. These sequences need only the first term to be defined. Find the common ratio. To find the third term, substitute the initial term and the second term into the formula. Well four minus one is just three, so it's going to be equal to b of three plus

Search for: Writing the Terms of a Sequence Defined by a Recursive Formula Sequences occur naturally in the growth patterns of nautilus shells, pinecones, tree branches, and many other natural structures.

All I did is said okay, well we're not trying to figure out, or we're not immediately trying to figure out what b of one is.

To find the third term, substitute the initial term and the second term into the formula. Each term of the Fibonacci sequence depends on the terms that come before it.

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. If b of two is equal to five, well then this is equal to five right over here, and then now we know that b of three is equal to five plus 12 which is equal to Their growth follows the Fibonacci sequence, a famous sequence in which each term can be found by adding the preceding two terms.

Instead, we describe the sequence using a recursive formula, a formula that defines the terms of a sequence using previous terms.

Constructing arithmetic sequences Video transcript - [Instructor] We are told b of one is equal to negative seven, and b of n is equal to b of n minus one plus 12, and they're asking us to find the fourth term in the sequence.

If we know that b of three is equal to 17, then we're ready to calculate what b of four is going to be. If we use the same definition, b of two is going to be equal to b of two minus one plus 12, so b of two minus one.

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