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: