Finding the nth Term of the Sequence


Uploaded by TheIntegralCALC on 06.03.2011

Transcript:
Hi Everyone! Welcome back to integralcalc.com. Today were going to be talking about how to
find the nth term of a sequence. And, what we mean by that is that we’re given a sequence,
in this particular example, it’s the sequence one, four, nine, sixteen, etcetera, on into
infinity, and they’re asking us to find the nth term. So, they’re asking us to provide
a formula that gives… that will give us any term in the sequence, just depending on
its order. So, the way that we’re going to do this is look for a pattern in our sequence.
And this is a really common problem for this particular kind of concept and term of the
sequence because notice that it’s… they’re all squares. So the first term is one squared,
the second term is two squared, then three squared, then four squared, so, that’s our
pattern right there. But just a kind of get an idea of how to do
this sort of problem, this is what’s going to look like. So, obviously, we’ve transformed
the sequence into one squared, two squared, three squared, four squared. Well, remember
that sequences usually start from the first term, n equal to one, so, that means it’s
the first term in the sequence, that means n is equal to one, the second term in the
sequence means that n is equal to two, and so on. So, you kind of want to find the relationship
to, you know, the pattern one, two, three, four, instead of the pattern you’re given
which, in our case, is one, four, nine, sixteen. And we’ve clearly done that here. We can
see the one, two, three, and four, so, that’s… that means that n is, you know, one, two,
three, and four. So when we… when we write out our sequence, here, you can see we have
a relation to n. If n is equal to one, then our first term is going to be one squared
which is one. If n is equal to two, the second term in our sequence, we’re going to get
two squared which is four. And, you can see that we’re going to follow the pattern of
our original sequence. So, this sequence that were given can actually
be written a sub n, which is sequence notation, equal to n squared and then we have to remember
that we’re going to start our sequence at one and has to start at one or something greater.
We could start at two, that will still apply, right, if we plug in two, we have four, that’s
still a member of our sequence here. But, we have to at least start at one; we can’t
start at zero or at any negative numbers. So, n must be greater than or equal to zero.
But, that’s kind of the general idea. I’m going to do a bunch of these problems. That’s
the general idea for finding sequences. Looking for the relationship to the sequence
one, two, three, four, as suppose to whatever you’re giving here, and, when we write these
as squared, we can really see the relationship one, two, three, four, and then, replace one,
two, three, four, with n. And, if we replace each of these with n, you can see the pattern
clearly is n squared. So, I hope that video helped you guys and
I’ll see you in the next one. Bye!