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# Worked example: sequence recursive formula

Video transcript

A sequence is defined
recursively as follows. So a sub n is equal to a sub n
minus 1 times a sub n minus 2. Or another way of
thinking about, the n-th term is equal to
the n minus 1-th term times the n minus 2-th term with
the 0-th term, or a sub is equal to 2 and a
sub 1 is equal to 3. Find a sub 4. So let's write this down. So they're telling us
a sub 0 is equal to 2. And they also tell us that
a sub 1 is equal to 3. So they've kind of given us our
starting conditions or our base conditions. Now, we can think
about what a sub 2 is. And they tell us that a sub 2
is going to be a sub 2 minus 1. So that's a sub 1. It's a sub 1 times
a sub 2 minus 2. Well, that's a sub 0. So a times a sub 0. And they already told us
what a sub 1 and a sub 0 is. This thing is 3. This thing is 2. So it's 3 times 2,
which is equal to 6. Now, let's move on to a sub 3. So a sub 3 is going to be the
product of the previous two terms. So it's going to be a sub 2. 3 minus 1 is 2, 3 minus 2 is 1. So it's a sub 2 times a sub 1. So it's equal to 6 times
3, which is equal to 18. And then finally, a sub 4,
which I'll do it in yellow. A sub 4 is going to be equal
to a sub 3 times a sub 2. So 4 minus 1 is
3, 4 minus 2 is 2. So times a sub 2-- do it in
that blue color-- times a sub 2, which is equal to 18 times 6,
which is equal to-- let's see, 6 times 8 is 48, or
6 times 10 is 108. And we're done, a sub
4 is equal to 108.