This is an example of an arithmetic sequence: 17, 11, 5, -1, -1,…

The common difference here is -6 because it goes down by 6 each time

to find , you need to find first. TO find you need the common difference (in this case it is -6) and do dn plus or minus however much you need to get to the first term. So for my example, it would be: -6n+23. Because then would be 17, which is the first term in the sequence. Now just put 50 in the equation.

= -6×50+23

= -277

Now, to find , the goal is to add all the numbers in the series together. To do that, all you have to do is add the first

term and the last term together first, then multiply it by the total number of terms in the series divided by two. Using my example above: [ + ] x 50/2 = [17+ (-277)] x 50/2

[ + ] x 50/2 = -6500.

And that is how to find of an arithmetic sequence and of and arithmetic series.