Category: Algebra

  • How to Find the nth Term in a Sequence

    How to Find the nth Term in a Sequence

    Kellie writes: “I am told to find the nth number in a pattern. What the heck does nth mean?”

    So I’ll first answer the question directly. Then we can talk about what it means to the rest of the problems.

    One more piece of the puzzle before we’re on to solve problems. I’ll bet you saw something in there about n-1 or n+1. Here’s a bit about that…

    Now let’s get into writing the nth term of a sequence using the one before it. Remember the nth term is the number in the list if you count up to whatever you’ve labeled n.

    In the previous video, we would have written it in fancy terms like this:

    xn=xn−1+2x_n = x_{n-1} + 2

    Once more, just to get the hang of it:

    Again, this one would have been written:

    xn=xn−1+4x_n = x_{n-1} + 4

    Aha! But what if you don’t know the number right before the one you want? Watch this:

    Still have questions? Post them in the comments.

    Thanks Kellie, for your question!

  • Using Conjugates in Imaginary and Complex Number Work

    Using Conjugates in Imaginary and Complex Number Work

    Complex numbers are made from one part real number and one part imaginary number. That’s one heck of a mixture.

    Anytime you mix things, you take the complicated to, well, the complex. (Goodness I’m punny today!)

    We use conjugates in the manipulation of these things. First it’s important to understand what a conjugate is…

    It’s just a pixie-dust quick-switch sleight of hand thing, right? Pretty much. Can you legally do that? Well, no. Clearly 4+8 is not the same as 4-8. Anymore than 12 is the same as -4. Duh.

    But you’ll see in this next video that you’re not really jumping up and trying to change the value of things…

    What’s really happening is that you’re inventing something to use as a “clever form of one” – the big fat one.

    And here’s one more example. Don’t forget to comment if you’re still confused.

  • A Quick Way to Learn Completing the Square

    A Quick Way to Learn Completing the Square

    Completing the square isn’t as hard as everyone thinks. And there’s no reason to memorize a bunch of strange pixie dust magic math rules. Here’s the way to see it for what it is.

    Here’s another example:

    This last one involves fractions:

    Have questions? Post them in the comments.

  • How to Solve an Equation with Four Terms

    How to Solve an Equation with Four Terms

    Do you ever wonder why teachers start a problem the way they do?

    There are four reasonable ways to start solving an equation like:

    3x + 2 = 4x – 1

    On this site I will always manipulate and move things around so that the equation we’re solving looks like:

    (the three colors represent three different numbers)

    I have done it here:

    Have questions? Post them in the comments.