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Maths Exercices
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: S_n=(a_1+a_n)/2•n
    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 21 terms of the arithmetic sequence where the first terms are: -3,0,3,6,...

Solution =