# Write an equation for the nth term of each arithmetic sequence

## Write an equation for the nth term of each arithmetic sequence

Practice Problems 1a - 1b: Find the first five terms and the 15th term of the given arithmetic sequence. Math works just like anything else, if you want to get good at it, then you need to practice it. What's the fourth term? If you said 99 give yourself a pat on the back. So our the th term in our sequence will be negative So we're going to have, this term right here is n minus one, so minus n minus one times six. When n is two, n minus one is one. We can use the n th term of an arithmetic sequence and solve for n , the number of terms in the sequence: Putting in 3 for the first term, 99 for the last term, and 33 for n Practice Problems These are practice problems to help bring you to the next level. So let's write it like this in a table. Now what's happening here?

So if we had the nth term, if we just had the nth term here, what's this going to be? So you could say this is 15 minus six times or let me write it better this way, minus zero times six. If you said 3 you are right! Then to go from nine to three, well we subtracted six again. This is 15 minus, we're subtracting the six three times from the 15, so minus three times six.

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

So our first term we saw is So 99 times six, actually you could do this in your head. So we are looking for the sum of terms 5 - Since this summation starts at 5, you need to plug in 5 into the given formula: What is the last term? It's going to be 15 minus, you see it's going to be n minus one right here, right when n is four, n minus one is three. If you said 3 you are right! What is the first term? Note how n starts at 5 and ends at Let me write this down just so, notice when your first term, you have 15 and you don't subtract six at all, or you could say you subtract six zero times. So this right here is , and then to figure out what 15, so we wanna figure out, we wanna figure out what 15 minus is, and this can sometimes be confusing, but the way I always process this in my head is I say that this is the exact same thing as the negative of minus So what's minus 15?

Six times nine is 54, carry the five. When n is two, n minus one is one.

What's 99 times six? If you start at 1 and go all the way to 20, there will be 20 terms. It will allow you to check and see if you have an understanding of these types of problems. I'll do a nice little table here. So what's minus 15? When n is one, n minus one is zero.

Now what's happening here?

### Arithmetic sequence formula

So in the third term, you subtract a six twice. We subtracted six again. You should do it, we could do this in our head. So you could say this is 15 minus six times or let me write it better this way, minus zero times six. What is the first term? So if you wanna figure out the th term of this sequence, I didn't even have to write it in this general term, you could just look at this pattern. The third term is going to be 12 minus from the first term, or six subtracted twice. Six times nine is 54, carry the five. If you said give yourself a pat on the back. So our first term we saw is What's the fourth term? Note how n starts at 5 and ends at Practice Problems 1a - 1b: Find the first five terms and the 15th term of the given arithmetic sequence. If you said 20, you are correct. Even the best athletes and musicians had help along the way and lots of practice, practice, practice, to get good at their sport or instrument.

So if we have the term, just so we have things straight, and then we have the value, and then we have the value of the term.

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