00:02
Okay, i've got the general formula for the nth term of an arithmetic sequence written at the top there.
00:11
And then we've got our first arithmetic sequence, goes 1 .4, 4 .5, then 7 .6.
00:19
And we want to know what is the 41st term.
00:24
So let's find the common difference.
00:28
In other words, how much does it go up by each, between each term? so i could do 4 .5 minus 1 .4, or i could notice that i've got to add 3 .1.
00:44
And then i could check to see is that the same difference for 4 .5 and 7 .6, and it is, it's 3 .1.
00:54
So that's our d value, our common difference.
00:58
So let's go ahead and write our formula for the nth term.
01:02
So we take our first term, 1 .4.
01:07
We add n minus 1 times our common difference.
01:15
So we could clean that up and simplify that.
01:19
We can also double check by plugging in, we could plug in like, say, 2 for n, and we get 2 minus 1, that'd be 1 times 3 .1.
01:32
So that'd be 3 .1 plus 1 .4, and we would get the second term of 4 .5.
01:39
But we want to plug in 41 for n.
01:45
We want to know the 41st term.
01:48
So let's do that.
01:51
Do 1 .4 plus 41 minus 1.
01:56
Well, that's 40 times 3 .1.
02:03
Then i'll just use my calculator to work that out.
02:08
So it's going to be 1 .4 plus 40 times 3 .1, and i get 125 .4 for the 41st term.
02:21
So let me erase that n, because now this is a 41.
02:33
Okay, let's look at number 2.
02:40
Number 2 was 9, 18, 27, and i want to know the 23rd...