# AP, GP and HP

Posted March 25, 2009

on:**Arithmetic Progression:**

*Example: *a, a+d, a+2d…..where ‘a’ is the first term and ‘d’ is the common difference.

*Nth Term: *a + (n-1)d

*Sum to N terms : *n/2 [2a + (n-1+d] or n/2[First Term + Last Term]

*AP of 3 terms: *a-d, a, a+d

*AP of 4 terms: a-3d, a-d, a+d, a+3*

**Geometric Progression:**

*Example: *a, ar, ar^2, ar^3….. where ‘a’ is the first term and ‘r’ is the common ratio

*Nth Term: *ar^(n-1)

*Sum to N terms: *[a((r^n) – 1)/r-1], signs change if r < 1.

*Sum to Infinity: *a/(1-r), if r<1

*3 terms of a GP: a/r, a, ar*

*4 terms of a GP: a/r^3, a/r, ar, ar^3
*

Tags: AP, Arithmetic progressions, Cat, Geometric Progression, GP, Harmonic progressions, HP, Mathematics, Maths, Quants, Series

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