Here's the cool thing: We're NOT going to have to keep making these tables! Since all arithmetic sequences behave the same way (change by adding a number), we can get a formula that works for ALL of them!
Check out the pieces of our last guy:
Let's check to see if this thing works on another arithmetic sequence:
How about this guy?
This would be the formula:
|Let's use it to find||:|
Now, let's check it the long way:
The cool thing is that you can use this formula to find the 2000th term: