Sequences, Progressions, Series, Means and Averages

Averages

  • Equation

  • Equation

Mean

  • Equation

  • Equation

  • Equation

For two numbers a and b, Equation

Arithmetic Progression

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

  • Equation

  • Equation

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

Geometric Progression

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

  • Equation

  • Equation

  • Equation

Harmonic Progression

  • Equation

Sum of Important Series

  • Sum of first n natural numbers: Equation

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

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