An important concept that comes from sequences is that of series and summation. Series and summation describes the addition of terms of a sequence. There are different types of series, including arithmetic and geometric series. Series and summation follows its own set of notation that is important to memorize in order to understand homework problems.
So a series is just the summation of a sequence. So a sequence is just a bunch of numbers in a row, a series is what happens when we add up all those numbers together. Okay?
So before me I have a general term for a sequence. a sub n is equal to n squared minus 1. And first we're asked to find the first four terms. Okay? So in order to find the first term, we would find a sub 1 which happens when we plug in 1. 1 squared minus 1 that's just 0. So our first term is going to be 0.
To find the second term we plug in 2. a sub 2 is equal to 2 squared. 4-1 which is going to give us 3. Third term [IB] and repeat a sub 3 is 3 squared, 9-1 is 8. And the fourth term a sub 4, plug in 4. 4 squared, 16-1 is 15.
So this right here is a sequence. It's 4 numbers written in order with commons in between. It's just a collection of numbers.
Find the sum of those first 4 terms. So basically we already found the 4 terms, all we have to do is add them together. 0+3 is 3 plus 8 is 11 plus 15 is 26. So 26 is then the series, okay? Series is the way I remember it is, series is a shorter word therefore your answer should be shorter, one number. A sequence is a longer word, it's going to be a collection of data, a collection of numbers, okay?
So basically all the series is is a summation of the sequence.