How do I find the sum of an arithmetic series?
- An arithmetic series is the sum of the terms of an arithmetic sequence
- The following formulae will let you find the sum of the first n terms of an arithmetic series:
- 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 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
- There will be n of these terms
- Divide by two as two of the sums have been added together
The arithmetic series formulae are in the formulae booklet – you don't need to memorise them.