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