Deriving the Formula of the Arithmetic Sequence

An arithmetic progression orĀ arithmetic sequence is a sequence of numbers such that the difference between two consecutive terms is constant. The sequence

3, 7, 11, 15, 19, 23, 27

is an example of an arithmetic sequence. The first term of the sequence above is 3, the constant difference is 5, and the 6th term or the last term is 27.

But what is its 100th term?

In “The Sum of the First n Positive Integers,” I have mentioned that if you want to be a mathematician someday, you will have to be good at seeing patterns. The problem above can be used to test or practice your skill in recognizing patterns. You might want to stop reading and see if you can answer the problem before proceeding. Continue reading