Sequences, Progressions, Series, Means and Averages

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Averages

Mean

For two numbers a and b,

Arithmetic Progression

  • An Arithmetic Progression (A. P.) with first term ‘a’ and Common Difference ‘d’ is given by: and nth term,

  • Sum of first ‘n’ terms, Sn (First Term + Last Term)

Geometric Progression

  • A Geometric Progression (G. P.) with first term ‘a’ and Common Ratio ‘r’ is given by: ar2 ar3 n-1 where th term,

Harmonic Progression

Sum of Important Series

  • Sum of first n natural numbers:

  • Sum of the squares of the first n natural numbers:

  • Sum of the cubes of the first n natural numbers: