Perhaps the simplest is to take the average, or arithmetic mean, of the first and last term and to multiply this by the number of terms.
A Sequence is a set of things (usually numbers) that are in order.
I'm just really copying this down, but I'm making sure we associate it with the right term.
So we went from the first term to the second term, what happened? It's always good to think about just how much the numbers changed by. So you could say this is 15 minus six times or let me write it better this way, minus zero times six. Or you could say plus one times negative six, either way, we're subtracting the six once. This is 15, this is 15 minus two times negative six, or sorry minus two times six, minus two times six. So if you see the pattern here, when our term, when we have our fourth term, we have the term minus one right there, the fourth term we have a three, the third term we have a two, the second term we have a one. So we're going to have, this term right here is n minus one, so minus n minus one times six.
An arithmetic sequence is one in which each term is separated from the one before it by a constant that you add to each term.
If you're seeing this message, it means we're having trouble loading external resources on our website. And then our fourth term, our fourth term is negative three.
If you're behind a web filter, please make sure that the domains *.and *.are unblocked. And they wanna ask, they want us to figure out what the 100th term of this sequence is going to be. So the second term is going to be six less than the first term. So whatever term you're looking at, you subtract six one less than that many times.
- [Instructor] We are asked what is the value of the 100th term in this sequence, and the first term is 15, then nine, then three, then negative three. 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. So let's see what's happening here, if we can discern some type of pattern. Then to go from nine to three, well we subtracted six again. And then to go from three to negative three, well we, we subtracted six again. The third term is going to be 12 minus from the first term, or six subtracted twice. 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. This is 15, it's just we just subtracted six once, or you could say minus one times six. This is 15 minus, we're subtracting the six three times from the 15, so minus three times six.
The second sequence isn't arithmetic because you can't apply this rule to get the terms; the numbers appear to be separated by 3, but in this case, each number is multiplied by 3, making the difference (i.e., what you'd get if you subtracted terms from each other) much more than 3.
In the first example, the constant is 3; you add 3 to each term to get the next term.