00:01
We're told that sn is equal to 3n minus, excuse me, 3n squared minus n.
00:17
Now, we have a formula for an, that's a plus n minus 1 times d.
00:33
We also have a formula for sn that's equal to n times the first term a, plus the nth term, which we just calculated, divided by two.
01:02
So here we have an equation that's true for each positive n, each n, each positive whole number n.
01:24
Okay, let's go ahead and simplify this.
01:29
We have 3n squared minus n equals n.
01:44
2a plus n d minus d divided by 2.
01:56
Okay, notice that we can divide each side by n.
02:06
So let's do that next.
02:12
N is the number of terms and the number of terms is positive.
02:20
So we can divide by n.
02:43
Okay.
02:46
Now let's go ahead and rewrite this one more time.
02:55
We'll write the right -hand side so that we have an n multiplied by d divided by 2, and then all the other stuff, which is 2a minus d divided by 2.
03:13
Okay.
03:15
Now let's go ahead and move the right...