# Write a formula for the nth term of the arithmetic sequence that models the percentage

### How to find the nth term of an arithmetic sequence

Write a formula for the time of her run after n weeks. So this one is not, not correct. And you might say, "Well, hey, these formulas look different. We started at 12, we subtract seven once. But then, we are going to subtract seven. This one over here is going to work. When "n" is four, we're adding 50 three times. We need to find the common difference, and then determine how many times the common difference must be added to the first term to obtain the final term of the sequence. So if "n" is one, it's going to negative , plus One, two times. And let's see if this actually works out.

It is, however, most common to subtract the first term from the second term because it is often the easiest method of finding the common difference. I want you to figure out what this needs to be so that if you input "n" here, it gives you the appropriate "f" of "n.

So that's all just going to be And it might be more than one. So we're going to subtract seven two times.

As with any recursive formula, the first term must be given.

Show Solution The situation can be modeled by an arithmetic sequence with an initial term of 1 and a common difference of 2.

And what I want you to do is pause the video, and think about which of these definitions of the function "f" are correct.

Now let's see about this one over here. If you were to take this first one, it's negativeplus, let's distribute this 50, plus 50 "n", plus 50 "n", minus It's going to be, we could think of it as we're starting at, The first term is going to be We can construct the linear function if we know the slope and the vertical intercept.

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