00:02
In this problem, we are asked to find an explicit formula that will give the same terms as this recursive formula of a sub 1 equals a sub n minus 1 plus n.
00:17
This is for all n greater than or equal to 2, and they've given us that a sub 1 is 1.
00:22
These are fun.
00:23
They're like puzzles.
00:25
You want to look for the pattern and see if you can write a formula that will give you that pattern.
00:29
You can see over on the left i made a little table that is what our n values are and then what the a value would be for that particular n.
00:40
And it took me a while to find the pattern for this.
00:43
I do encourage you to spend the time to find it because it's worth the effort.
00:49
What i finally decided was to look for something where i'm multiplying because i see that i'm adding repeatedly.
00:59
Repeated adding is multiplication.
01:02
The number that i want to use is whatever our n is.
01:06
So what i decided to do is what do i have to multiply n by to get the a.
01:12
It's associated with that n.
01:13
So the first one is going to be one times one.
01:18
The second one, if n is two, a is three.
01:23
So the thing i will have to multiply two by is three over two.
01:31
The third one, the third one, one, n is 3.
01:36
If i multiply 3 times 2, i get 6.
01:39
The next 1 is 4...