Sum of Arithmetic Progressions (Cambridge (CIE) A Level Maths): Revision Note

Arithmetic Series

How do I find the sum of an arithmetic progression?

• The sum of the terms of an arithmetic progression is sometimes called an arithmetic series

• The following formulae will let you find the sum of the first n terms of an arithmetic progression:

     or   

  • a is the first term

  • d is the common difference

  • l is the last term

• You can use whichever formula is more convenient for a given question

• The a and the d in those formulae are exactly the same as the ones used with arithmetic progressions

How do I derive the formula for the sum of an arithmetic progression?

• Learn this proof of the sum of an arithmetic progression formula – you can be asked to give it on the exam:

  • Write the terms out once in order

  • Write the terms out again in reverse order

  • Add the two sums together

    • The terms will pair up to give the same sum 

    • There will be n of these terms

  • Divide by two as two of the sums have been added together