# How to write a recursive formula from explicit

When writing the general expression for an arithmetic sequence, you will not actually find a value for this. Find a10, a35 and a82 for problem 4. Find the explicit formula for 5, 9, 13, 17, 21.

Is a term in the sequence 4, 10, 16, 22. Find the explicit formula for 15, 12, 9, 6. We have d, but do not know a1. Now we have to simplify this expression to obtain our final answer. If neither of those are given in the problem, you must take the given information and find them.

Now that we know the first term along with the d value given in the problem, we can find the explicit formula. However, the recursive formula can become difficult to work with if we want to find the 50th term. Examples Find the recursive formula for 15, 12, 9, 6. To find the 50th term of any sequence, we would need to have an explicit formula for the sequence.

You must also simplify your formula as much as possible. The recursive formula for an arithmetic sequence is written in the form For our particular sequence, since the common difference d is 4, we would write So once you know the common difference in an arithmetic sequence you can write the recursive form for that sequence. You must substitute a value for d into the formula. Since we already found that in Example 1, we can use it here. 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.

In this situation, we have the first term, but do not know the common difference. In this lesson, it is assumed that you know what an arithmetic sequence is and can find a common difference.

There must be an easier way. Notice that an the and n terms did not take on numeric values. The explicit formula is also sometimes called the closed form. 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. If you need to review these topics, click here. Using the recursive formula, we would have to know the first 49 terms in order to find the 50th. This sounds like a lot of work. But if you want to find the 12th term, then n does take on a value and it would be 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. To find out if is a term in the sequence, substitute that value in for an. Write the explicit formula for the sequence that we were working with earlier. Look at it this way. However, we do know two consecutive terms which means we can find the common difference by subtracting.

Find the recursive formula for 5, 9, 13, 17, 21. There can be a rd term or a th term, but not one in between. Site Navigation Arithmetic Sequences This lesson will work with arithmetic sequences, their recursive and explicit formulas and finding terms in a sequence. To find the explicit formula, you will need to be given or use computations to find out the first term and use that value in the formula.

For example, when writing the general explicit formula, n is the variable and does not take on a value.I have this recursive function: f(n) = 2 * f(n-1) + 3 * f(n-2) + 4 f(1) = 2 f(2) = 8 I know from experience that explicit form of it would be: f(n) = 3 ^ n - 1 // pow(3, n) - 1 I wanna know if there's any way to prove that.

I googled a bit, yet didn't find anything simple to understand. To find the explicit formula, you will need to be given (or use computations to find out) the first term and use that value in the formula.

n is treated like the variable in a sequence. For example, when writing the general explicit formula, n is the variable and does not take on a value. In this lesson you will learn how to create a recursive formula by using what we know about function notation. Jan 11,  · Explicit formula is used to find the nth term of the sequence using one or more preceding terms of the sequence. Recursive and Explicit Formulas – Example Problems Example 1: First term of the sequence a1 = 28, common difference d = 14, find the recursive formula of the arithmetic sequence.

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? In this lesson you will learn how to write an explicit formula by using what we know about function notation. Create your free account Teacher Student.

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