00:01
So we're asked to look at a few sequences and determine the recursive definition.
00:06
So remember, recursive means we use the previous term.
00:10
So let's look at 35.
00:12
We see we have 1, 3, 5, 7, 9.
00:17
So we want to ask ourselves, what's happening? here we add 2.
00:22
Here we add 2.
00:24
Here we add 2.
00:25
Here we add 2.
00:26
So we can see it's the previous term plus 2.
00:29
So our sequence, we could write it as a sub n equals a sub n minus 1 plus 2, where a sub 0 equals 1.
00:43
So this would be for 35.
00:49
So let's look at 36.
00:51
We have 2, 4, 6, 8, 10.
00:58
So here we add 2, here we add 2, here we add 2, here we add 2, here we add 2, here we add 2, so our recursive definition is going to look very similar.
01:09
We're going to have a to the n equals a to n minus 1 plus 2, but in this case, our first term is equal to 2.
01:17
So a0 equals 2.
01:24
So let's look at number 37.
01:29
We have 3, 5, 9, 17, and 33.
01:37
So we see here we add two, here we add four, here we add eight, here we add 16.
01:56
So if you notice this is two to the first, this is two square, this is two to the third, this is two to the fourth, this is two to the fourth.
02:10
So we take our previous term and we add two to a power.
02:15
So here, this is term zero, this is term one, this is a0, this is a1, this is a2, this a3, this is a4, so we always add 2 to the power of n.
02:37
So this is going to be a sub n equals a sub n minus 1 plus 2 to the n.
02:49
Equal to three.
02:55
So you see this is our end term right here.
02:58
We see they match...