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