Mathematics (AS)·Sequences and series · NSSCAS 1.2.2
Arithmetic progressions
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Some number patterns climb by the same amount every step — those are arithmetic progressions, and they are exam favourites. In this lesson you will learn to spot an AP instantly, leap straight to its 20th or 200th term with the nth-term formula, and add up long lists of terms in seconds using Gauss's famous sum formula. We finish with a real Namibian savings problem, solved exactly the way the examiner wants it.
What you'll learn in this lesson
By the end you should be able to (NSSCAS Mathematics (AS) 1.2.2):
- Recognise arithmetic progressions by testing for a constant common difference.
- Use the formula for the nth term, uₙ = a + (n−1)d, to solve problems.
- Use the sum formulas Sₙ = n/2 (2a + (n−1)d) and Sₙ = n/2 (a + l) to solve problems involving arithmetic progressions.
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