Look for and make use of structure.

It may be the case with geometric sequences that the graph will increase or decrease. In most geometric sequences, a recursive formula is easier to create than an explicit formula.

The common ratio is usually easily seen, which is then used to quickly create the recursive formula. To summarize the process of writing a recursive formula for a geometric sequence: Determine if the sequence is geometric Do you multiply, or divide, the same amount from one term to the next?

Find the common ratio. The number you multiply or divide. Create a recursive formula by stating the first term, and then stating the formula to be the common ratio times the previous term.

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.

The sequence shown in this example is a famous sequence called the Fibonacci sequence. Is there a pattern for the Fibonacci sequence? After the first two terms, each term is the sum of the previous two terms. Is there a recursive formula for the Fibonacci sequence?This lesson will work with arithmetic sequences, their recursive and explicit formulas and finding terms in a sequence.

In this lesson, it is assumed that you know what an arithmetic sequence is and can find a common difference. If you need to review these topics, click here.

· Given the sequence: {6, 16, 26, 36, } a) Write an explicit formula for this sequence. b) Write a recursive formula for this regardbouddhiste.com · Write a recursive formula to generate each sequence. Then find the indicated term. a. 15, 11, 7, 3, Find the 10th term. Lesson • Recursively Defined Sequences Name Period Date.

1. Find the common ratio for each sequence. a.

42, Write a recursive formula for each sequence in Exercise 1 and find the 6th term. Use regardbouddhiste.com Let’s go back and look at the sequence we were working with earlier and write the explicit formula for the sequence.

2, 6, 18, 54, , The first term in the sequence is 2 and the common ratio is regardbouddhiste.com?file=regardbouddhiste.com A recursive formula allows us to find any term of an arithmetic sequence using a function of the preceding term.

Each term is the sum of the previous term and the common difference. For example, if the common difference is 5, then each term is the previous term plus regardbouddhiste.com://regardbouddhiste.com A recursive sequence is a sequence in which terms are defined using one or more previous terms which are given.

If you know the n th term of an arithmetic sequence and you know the common difference, d, you can find the (n + 1) th term using the recursive formula a n + 1 = a n + regardbouddhiste.com://regardbouddhiste.com /topics/recursive-sequence.

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Ninth grade Lesson Arithmetic vs. Geometric Sequences