 Hi, and welcome to this first in a series of videos on solving first and second order linear homogeneous recurrence relations. The sole purpose of this video is simply to make sure we are clear on each of the words that you just heard in the title. So first of all, we know what a recurrence relation is. It's a recursive definition for an integer sequence where the first few terms are given directly, and then later terms are given by computing them in terms of previous terms. For example, all the equations you see on the screen here are recurrence relations. The order of a recurrence relation refers to the maximum number of steps backwards we have to take in order to do the recursion. We're only going to be concerned for now with recurrence relations of orders one and two. The only ones up here on the screen that have orders one and two are these. Now let's define the remaining terms linear and homogeneous. Homogeneous just means that every term in the recurrence relation has at least one a on it, one element of the sequence. Of the ones on the screen, these are homogeneous. These others here are not homogeneous because there is at least one term in the sum that does not have a term of the sequence multiplied to it. Finally, when we say that a homogeneous recurrence relation is linear, what we mean is that when we look at all the terms, the only thing being done to the a terms and the elements of the sequence is multiplication by a constant that is a number. Of the recurrence relations you see here, only these are linear. These others are not linear because there is more being done to the sequence terms than just multiplication by a constant. For example, this one has a square root on the sequence term and this one here is being multiplied by n and n is not a constant. So the recurrence relations you see now are the only ones that are first or second order homogeneous and linear. In the remaining videos, we're going to explore an algebraic technique for finding closed formula solutions to first and second order homogeneous linear recurrence relations. Thanks for watching.