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Arithmetic series Edexcel International GCSE Mathematics A revision

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In plain words

A sequence that goes up by the same amount each time is called arithmetic. Adding its terms together gives a series. There's a formula for the total, so you can add the first hundred terms in one line.

Three things to know

  1. An arithmetic sequence has first term a and common difference d. Its nth term is a + (n − 1)d.
  2. The sum of the first n terms is Sₙ = n/2 × (2a + (n − 1)d).
  3. To use either formula, write down a, d and n first.

Worked example

Find the sum of the first 20 terms of 3, 7, 11, 15…

  1. a = 3, d = 4, n = 20.
  2. S₂₀ = 20/2 × (2 × 3 + 19 × 4) = 10 × (6 + 76).
  3. = 820.

Tips and tricks

  • It's (n − 1)d, not nd. The first term has no d's added to it.
  • d can be negative, for a sequence that goes down.
5 questions, about 2 minutes.

It lands in your notebook with its questions as flashcards.

Arithmetic series: 5 questions and answers

These are the quiz’s questions. Do the quiz first, then come back here for the ones that got you.

  1. What is the common difference of 4, 9, 14, 19?
    • 4
    • 5 (the answer)
    • 9
    • 10

    Each term is 5 more than the one before.

  2. What is the 10th term of 2, 6, 10, 14?
    • 36
    • 38 (the answer)
    • 40
    • 42

    2 + 9 × 4.

  3. In Sₙ = n/2 × (2a + (n − 1)d), what is a?
    • the first term (the answer)
    • the last term
    • the common difference
    • the number of terms

    d is the common difference and n the number of terms.

  4. What is the sum of the first 5 terms of 1, 3, 5, 7, 9?
    • 16
    • 20
    • 25 (the answer)
    • 45

    5/2 × (2 + 8).

  5. An arithmetic sequence has a = 10 and d = −2. What is its 4th term?
    • 2
    • 4 (the answer)
    • 6
    • 16

    10 + 3 × (−2).

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