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Video: Writing a Formula for the General Term of an Arithmetic Sequence and Using It to Find the Value of a Term in This Sequence

Kathryn Kingham

Jesse started a new exercise regimen. On the first day, he did 2 sit-ups, and, each day after that, he did 2 more sit-ups than the previous day. If this pattern continues, it forms an arithmetic sequence. Write the formula for its 𝑛th term, and then determine the total number of sit-ups he did on the twentieth day.

02:48

Video Transcript

Jesse started a new exercise regimen. On the first day, he did two sit-ups, and each day after that, he did two more sit-ups than the previous day. If this pattern continues, it forms an arithmetic sequence. Write the formula for its 𝑛th term, then determine the total number of sit-ups he did on the twentieth day.

Let’s highlight some of the information that’s given to us, that’s important for solving this problem. He did two sit-ups on the first day. Every day after that, two more than the previous day. And we formed an arithmetic sequence. The question is asking us for a formula that uses the 𝑛th term, and is asking for the total number of sit-ups on the twentieth day.

Let’s make a little chart here to show the day compared to the number of sit-ups that Jesse did. Here’s what that would look like: Day one, two sit-ups; day two, four sit-ups; day three, six sit- six sit-ups. On the bottom, we have this pattern of Jesse adding two sit-ups every day to the previous day. But do you see a correlation, a relationship, or a pattern between the number of the day and the sit-ups? If you take the day and you multiply it by two, you get the number of sit-ups that Jesse should be doing that day. This means, if we take our 𝑛th day and multiply it by two, we will find out how many sit-ups Jesse should do to the 𝑛th term. Two 𝑛 equals the number of sit-ups that Jesse needs to do on day 𝑛. This is the formula that will always work. It’s the formula for the 𝑛th term.

Our work here is not done. We also need to determine the total number of sit-ups that Jesse did on the twentieth day. Our formula tells us that we multiply the day by two. Twenty times two equals forty. Jesse should do forty sit-ups on day twenty.

Two 𝑛 is our formula and the twentieth day total is forty sit-ups.