Sum of a Geometric Progression

What is Sum of a Geometric Progression?

The total of the first n terms of a sequence with a constant common ratio. It equals a multiplied by one minus r to the power n, all divided by one minus r, where a is the first term and r the common ratio, and it is valid only when r is not equal to one. The equivalent form a times r to the power n minus one, all over r minus one, is the same expression with the signs of numerator and denominator both reversed. When r equals one every term is a, so the sum is n times a.

This definition is part of the Series chapter in Cambridge O Level Additional Mathematics.

Concepts related to Sum of a Geometric Progression

• common ratio
• the r = 1 exception
• partial sum
• Sum to Infinity