Look at the example below to see what happens. 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. To write the explicit or closed form of an arithmetic sequence, we use an is the nth term of the sequence.
The way to solve this problem is to find the explicit formula and then see if is a solution to that formula. Rather than write a recursive formula, we can write an explicit formula. There can be a rd term or a th term, but not one in between.
Now we have to simplify this expression to obtain our final answer. What is your answer? 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. However, the recursive formula can become difficult to work with if we want to find the 50th term.
You must also simplify your formula as much as possible. To find the 50th term of any sequence, we would need to have an explicit formula for the sequence. You will either be given this value or be given enough information to compute it.
The first term in the sequence is 20 and the common difference is 4.
If neither of those are given in the problem, you must take the given information and find them. Notice that an the and n terms did not take on numeric values.
Using the recursive formula, we would have to know the first 49 terms in order to find the 50th.
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. Well, if is a term in the sequence, when we solve the equation, we will get a whole number value for n.
There must be an easier way. If we do not already have an explicit form, we must find it first before finding any term in a sequence.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. a) Write an explicit formula for this sequence.
b) Write a recursive formula for this sequence. Sal shows how to evaluate a sequence that is defined with a recursive formula. This definition gives the base case and then defines how to.
Section Using Recursive Rules with Sequences A recursive rule gives the beginning term(s) of a sequence and a recursive equation that tells how a n is related to one or more preceding terms. Evaluating a Recursive Rule Write a recursive rule for the sequence whose graph is shown.
7. 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. write explicit formulas for arithmetic sequences write linear equations in intercept form same sequence.
Recursive formula Explicit formula u 0 5 u n 5 7n u n u n 1 7 where n 1 Lesson † Linear Equations and Arithmetic Sequences (continued).Download