Week 1 – Precalc 11

This week in math we learned about arithmetic sequences, to be specific how to find a specific term in a sequence using an equation. To begin, a sequence is a set of numbers. For a sequence to be arithmetic, it has to go up by the same number each time, or in other words, have a common difference.

Say we have a sequence: 2, 4, 6, 8, 10, 12. The common difference is 2. If we want to find the 100th term, we need to use the equation: $t_n$ = $t_1$+(n-1)d. We are trying to find the 100th term, so $t_n$=$t_{100}$. Next, $t_1$ is the first term in the sequence, so it’s $t_1$=2. And we already know what n is, 100. Now, we plug into these numbers into the equation. $t_{100}$=2+(100-1)(2). You can now try to solve this and will find what the 100th term in the sequence is. To check your answer: the 100th term in the sequence is 200, which is found by solving the equation.

You can also use the equation to find different things, just plug all the numbers you have into the equation and as long as there is only one unknown variable, you can find the answer.

Some important notes to take from this:

It is essential to have a common difference in a sequence of numbers for it to be arithmetic, if there is no common difference this equation won’t work. The equation is $t_n$=$t_1$+(n-1)d, this equation is very important! Answer it step by step if needed too, it can help you organize your thoughts if you find this confusing. I’ve included a picture example below of another question this equation can be used to answer.