# 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 n

^{th}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: ar2ar3n-1where 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: