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Arithmetic and geometric sequences
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
Sn = sum of the first n terms
Sometimes we use:

Find the sum of the first 40 terms, s40 of 3, 7, 11, 15,...

 Compute the sum of the first 26 terms of the arithmetic sequence where a2 = -7 and a3 = -12

Solution =