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- [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.
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.
And this is actually going to be the case for n greater than one.
For n equals one, s sub one is going to be, well you can just, a sub one is going to be equal to s sub one.
Now if I wanna figure out a sub n, which is the goal of this exercise, well I could subtract out the sum of the first n minus one terms. So that is s, that is s sub n minus one, and what would that be equal to.
Well wherever we see an n, we'd replace with an n minus one.
But if you didn't wanna do it that way, you just do it the old-fashioned way. Negative one times 594 is negative 594, negative one times negative 15 is positive 15.
I'm just really copying this down, but I'm making sure we associate it with the right term.But then for any other n, we could use this right over here.