Arithmetic Series (OCR A Level Maths: Pure)

Revision Note

Roger

Author

Roger

Last updated

Did this video help you?

Arithmetic Series

How do I find the sum of an arithmetic series?

  • An arithmetic series is the sum of the terms of an arithmetic sequence

Arithm Series Illustr, A Level & AS Level Pure Maths Revision Notes

  • The following formulae will let you find the sum of the first n terms of an arithmetic series:
S subscript n equals n over 2 left parenthesis 2 a plus left parenthesis n minus 1 right parenthesis d right parenthesis   or   S subscript n equals n over 2 left parenthesis a plus l right parenthesis
    • is the first term
    • is the common difference
    • 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 sequences

 

How do I derive the arithmetic series formula?

  • Learn this proof of the arithmetic series 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 2 a plus left parenthesis n minus 1 right parenthesis d
      • There will be of these terms
    • Divide by two as two of the sums have been added togetherArithm Series Proof, A Level & AS Level Pure Maths Revision Notes

Examiner Tip

The arithmetic series formulae are in the formulae booklet – you don't need to memorise them.

Worked example

Arithm Series Example, A Level & AS Level Pure Maths Revision Notes

You've read 0 of your 10 free revision notes

Unlock more, it's free!

Join the 100,000+ Students that ❤️ Save My Exams

the (exam) results speak for themselves:

Did this page help you?

Roger

Author: Roger

Expertise: Maths

Roger's teaching experience stretches all the way back to 1992, and in that time he has taught students at all levels between Year 7 and university undergraduate. Having conducted and published postgraduate research into the mathematical theory behind quantum computing, he is more than confident in dealing with mathematics at any level the exam boards might throw at you.