Arithmetic series
An
arithmetic series is the sum of an aritmetic sequence. That is,
a1+a2+a3+...+an=a1+a1+d+a1+2d+a1+3d+...+a1+(n-1)d
The series 3 + 7 + 11 + 15 + 19 + ... + 99 is an aritmetic series which first term is a1=3 and the common difference is d=4.
To solve exercises using aritmetic sequences you need the following formulas:
- The nth term: an= a1+ (n-1) d
-
The sum of the first n terms: 
where:
a1 = the first term of the sequence
d = common difference (Remember you can obtain it using
d=an-
an-1 or
.)
n = number of terms
an =
nth term
S
n = sum of the first
n terms
Sometimes we use:
