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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.