General Forms of a Sequence

General Forms Of A Sequence:

~Sequence: series (list) of numbers

~Arithmetic:  sequence of numbers such that the difference between the consecutive terms is constant.
            
             -example-  5,7,9,11,13,15... is an arithmetic sequence with a                               difference of 2.

             -formula-  a_n=  a₁+(n-1)d                    d=a_n-a_n-1

                                            _{d= common difference}

~Geometric: sequence of numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.
             -example-  2,6,18,54... is a geometric sequence with a common                      ratio of 3.

             -formula-  a_n=a_{1 x} r^n-1                                  r= a_n ÷ a_n-1

                                                      _{r= common ratio}