Today we learned about arithmetic sequences, which is a sequence whose consecutive terms have a common difference. An easy way to find out if a sequence is arithmetic is by subtracting the first term from the second term. This will be the common difference, if the common difference is sustained throughout the whole sequence, then it is an arithmetic sequence.
In order to find the nth term of an arithmetic sequence, all you have to do is keep adding numbers until you get to that term! Just kidding, there's a formula (because there's one for everything!) and it makes things so much easier.
The formula is An = A1 + (n-1)d
A1 is the first term of the sequence. N is the number term you want to find. And d is the common difference.
Here's an example!
In addition to arithmetic sequences, there is the sum of arithmetic sequences! And of course, there is a formula!
The formula is Sn = n/2(A1 + An)
N would be the last term you want to find. Then A1 is the first term and An would be the last term. But, something that most people get confused with is putting the number of the term in An, when it is supposed to be the actual term. So you must find the actual term first by using the explicit formula. Here is an example:
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