# How to write a recursive formula for a sequence

Now that we know the first term along with the d value given in the problem, we can find the explicit formula. What is your answer? What happens if we know a particular term and the common difference, but not the entire sequence?

This is enough information to write the explicit formula. Site Navigation Arithmetic Sequences This lesson will work with arithmetic sequences, their recursive and explicit formulas and finding terms in a sequence.

This is enough information to write the explicit formula. In this situation, we have the first term, but do not know the common difference.

Find the explicit formula for 0. 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. Now we have to simplify this expression to obtain our final answer.

You must substitute a value for d into the formula.

This sounds like a lot of work. Find the recursive formula for 5, 9, 13, 17, 21.

Notice this example required making use of the general formula twice to get what we need. However, we have enough information to find it. But if you want to find the 12th term, then n does take on a value and it would be Now that we know the first term along with the r value given in the problem, we can find the explicit formula.

Using the recursive formula, we would have to know the first 49 terms in order to find the 50th. However, we do know two consecutive terms which means we can find the common ratio by dividing.

Look at the example below to see what happens. Find a6, a9, and a12 for problem 8. 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.

The explicit formula is also sometimes called the closed form. For example, when writing the general explicit formula, n is the variable and does not take on a value.

To find out if is a term in the sequence, substitute that value in for an. Find a6, a9, and a12 for problem 4. The formula says that we need to know the first term and the common ratio. Order of operations tells us that exponents are done before multiplication. Since we already found that in our first example, we can use it here.

Is a term in the sequence 4, 10, 16, 22. To find the 50th term of any sequence, we would need to have an explicit formula for the sequence.

This sounds like a lot of work. Find the explicit formula for 5, 10, 20, 40. In this situation, we have the first term, but do not know the common ratio. Rather than write a recursive formula, we can write an explicit formula. Using the recursive formula, we would have to know the first 49 terms in order to find the 50th.

Find the explicit formula for 15, 12, 9, 6. To find the 10th term of any sequence, we would need to have an explicit formula for the sequence. If neither of those are given in the problem, you must take the given information and find them. If neither of those are given in the problem, you must take the given information and find them.

We have d, but do not know a1. Rather than write a recursive formula, we can write an explicit formula. If we do not already have an explicit form, we must find it first before finding any term in a sequence.The recursive formula for a geometric sequence is written in the form For our particular sequence, since the common ratio (r) is 3, we would write So once you know the common ratio in a geometric sequence you can write the recursive form for that sequence.

a) Write an explicit formula for this sequence. b) Write a recursive formula for this sequence. The sequence of second differences is constant and so the sequence of first differences is an arithmetic progression, for which there is a simple formula.

A recursive equation for the original quadratic sequence is then easy. A recursive sequence is a sequence in which terms are defined using one or more previous terms which are given.

you can find the (n + 1) th term using the recursive formula a n + 1 = a n + d. Write the first four terms of the geometric sequence whose first term is a 1 = 3 and whose common ratio is r = 2.

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. There. 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 .

How to write a recursive formula for a sequence
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