9.2 arithmetic sequence

Today lets go into arithmetic sequences!

Definition: the difference between consecutive terms are the same! 

      A2-A1=A3-A2= A4-A3=d

How to find the nth term

      An= dn+c

       (c= a1-d)

Ex: find a formula for the nth term of the sequence with d= 3 and a1= 2

An= 3n+c 

C= 2-3= -1

An= 3n-1

The sum of a finite arithmetic sequence:

An= n/2(a1+an)

Ex: find the sum of intergers from 1 to 100

Sn= 100/2* (1+100)= 5050