My-riflessiones

AP, GP and HP

Posted on: March 25, 2009

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

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