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Year 11 · Patterns & Algebra

Arithmetic sequences and series

An arithmetic sequence adds the same amount each time; a geometric sequence multiplies by the same amount.

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How to do it

  1. Arithmetic: nth term = a + (n − 1)d, sum = n/2 (2a + (n − 1)d).
  2. Geometric: nth term = a × rⁿ⁻¹, sum = a(rⁿ − 1) ÷ (r − 1).

Worked example

What is the 18th term of 8, 15, 22, 29, …
Each term goes up by d = 7. Tₙ = a + (n − 1)d = 8 + 17 × 7 = 127.
Answer: 127

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Watch out
Use n − 1, not n, in the nth-term formula.

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