Writing a recursive formula for sequences

Notice this example required making use of the general formula twice to get what we need. However, we have enough information to find it. Write the explicit formula for the sequence that we were working with earlier.

This sounds like a lot of work. So writing a recursive formula for sequences explicit or closed formula for the arithmetic sequence is. This will give us Notice how much easier it is to work with the explicit formula than with the recursive formula to find a particular term in a sequence.

However, we do know two consecutive terms which means we can find the common difference by subtracting. In this lesson, it is assumed that you know what an arithmetic sequence is and can find a common difference. Recursive equations usually come in pairs: Examples Find the recursive formula for 15, 12, 9, 6.

For example, when writing the general explicit formula, n is the variable and does not take on a value. This arithmetic sequence has a common difference of 4, meaning that we add 4 to a term in order to get the next term in the sequence.

Find the recursive formula for 5, 9, 13, 17, 21. The way to solve this problem is to find the explicit formula and then see if is a solution to that formula.

Since we already found that in Example 1, we can use it here. Given the sequence 20, 24, 28, 32, 36. Rather than write a recursive formula, we can write an explicit formula. To find the 50th term of any sequence, we would need to have an explicit formula for the sequence.

Since our recursion uses the two previous terms, our recursive formulas must specify the first two terms.

There must be an easier way. The first term is 2, and each term after that is twice the previous term, so the equations are: In this situation, we have the first term, but do not know the common difference. The first time we used the formula, we were working backwards from an answer and the second time we were working forward to come up with the explicit formula.

What is your answer?

To find out if is a term in the sequence, substitute that value in for an. This sequence is called the Fibonacci Sequence. The first term in the sequence is 20 and the common difference is 4.

We already found the explicit formula in the previous example to be. Find a10, a35 and a82 for problem 4. Using the recursive formula, we would have to know the first 49 terms in order to find the 50th. Site Navigation Arithmetic Sequences This lesson will work with arithmetic sequences, their recursive and explicit formulas and finding terms in a sequence.

The first term of the sequence is 5, and each term is 2 more than the previous term, so our equations are: Now we have to simplify this expression to obtain our final answer.

Write recursive equations for the sequence 1, 1, 2, 3, 5, 8, 13, What does this mean? Look at it this way.Learn how to find recursive formulas for arithmetic sequences. For example, find the recursive formula of 3, 5, 7, If you're seeing this message, it means we're having trouble loading external resources on.

There are 80 fish in a Koi pond. Each year the population decreases by 25%. Which explicit formula generates a sequence of fish in the pond each year?

Find the recursive formula of an arithmetic sequence given the first few terms. If you're seeing this message, it means we're having trouble loading external resources on our website.

Practice: Recursive formulas for arithmetic sequences. Explicit formulas for arithmetic sequences. Explicit formulas for arithmetic sequences. So once you know the common difference in an arithmetic sequence you can write the recursive form for that sequence.

However, the recursive formula can become difficult to work with if we want to find the 50 th term. Using the recursive formula, we would have to know the first 49 terms in order to find the 50 th. This sounds like a lot of work. Take another look at the last sequence in the previous section: Find the next term in the following sequence: 1, 4, 8, 13, 19, 26, (1 / 2)(7) 2 + (3 / 2)(7) – 1 = 49 / 2 + 21 / 2 – 1 = The formula we found for the terms was a bit messy, what with the fractions.

A recursive formula allows us to find any term of a geometric sequence by using the previous term. Each term is the product of the common ratio and the previous term.

Recursive Sequences

Each term is the product of the common ratio and the previous term.

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Writing a recursive formula for sequences
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