How to Solve First Order Recurrence Relations

In subject of mathematics, a recurrence relation can be defined as a relation that recursively defines a sequence or multi-dimensional array of values. For example, x_n+1= rx_n (1-x_n) is an example of recurrence relation.  In it once or more initial terms are given to you and each further term of the sequence or array is defined as function of the preceding terms. It can be a part of differential equation and we study this concept of Mathematics after ninth grade. In order to be able to solve a recurrence relation, you need not adopt any special approach, but a bit of knowledge will solve your jeopardy. In order to solve a recurrence relation, you can bring following tips in use:-

How to Solve Recurrence Relations

1. Never Leave the Initial Part of Chapter:-

Most of us are very much habitual to leave the initial part of the chapter which is of introduction. If you have left this part of chapter for all other chapters in your book, I will insist you to read it for the chapter of recurrence relations. This part of the chapter will make you familiar with the structure, formation and analysis of a particular recurrence relation and thus you will be able to solve it in a better way.

2. Make Yourself Aware with the Formulas and Identities:-

Besides the first or initial portion of your chapter, you should never leave even the last portion of this chapter as well. The last portion of this chapter will have a page reserved for identities and formulas which can be bought in use when you solve the chapter. This page will be surely there if your book is an N.C.E.R.T prescribed book, but you can find it with the most of private books as well.

3. Don’t Skip the Lessons:-

Besides this, you should never skip lessons of your class as when you won’t know the basics, you won’t be able to solve recurrence relations. If you have already skipped some of your classes, I would request you to start from the basics once again. Basics serve to be the base of a particular chapter and when once basics get cleared, everything else related to the chapter also gets cleared like wisely.

4. Begin Step By Step:-

Begin forward step by step. Never try to solve the big or bulky questions in a single go but instead try to solve the easy initial questions of the exercise first of all. You can also take the help of solved examples if needed. Examples serve to be the best demonstration of how a particular kind of question needs to be solved and thus they are always your best friend in such cases.

5. Keep Formulas Ready by Your Side:-

You can also manage to keep formulas and identities written on a spare sheet of blank paper to keep it by your side so that you may not have to turn the pages again and again in order to check them. Besides this, you should take the help of a reference book if needed. Keep learning step by step and keep increasing the level of difficulty by solving more and more new questions researching them from the internet.

6. Know About A Recurrence Formula:-

For any sequence, say a_1,   a_2,  a₃……………………………a_n, the recurrence formula will be a set of rules that requires the computation of all previous terms in order to find the value of a_n. Let me give you a simple example of what recurrence relation is. Suppose if we take a_n= 2+3_n and if we are told that a_n is equal to “5”, then the value of 2+3_n should be “5” which gives the value of “n” as 1 when we solve the equation.

If we look at the example of a recurrence relation that I had given you in the very beginning of this topic, say. x_n+1= rx_n (1-x_n), it will be the same kind of relationship but the difference is just that it has been made somewhat complicated. When you will study the rest of formulas and when you will implement them, even these complicated relations will become easy to be solved for you.