Sum of an Arithmetic Progression

What is Sum of an Arithmetic Progression?

The total of the first n terms of a sequence with a constant common difference. It equals n over two multiplied by the bracket two a plus n minus one d, where a is the first term and d the common difference; equivalently it is n over two multiplied by a plus l, where l is the last term included. The second form is derived by writing the series forwards and backwards and pairing the columns, each of which totals a plus l.

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

Concepts related to Sum of an Arithmetic Progression

• common difference
• last term l
• pairing argument
• term versus sum