Foundation and Higher · special sequences
Four sequences
you must spot
on sight.
squares, triangles,
cubes, Fibonacci
these turn up everywhere, so —
Recognise
you are expected to know them
not work them out each time
sequence 1 of 4
Square numbers
1. Dots in a square: 1 × 1, 2 × 2, 3 × 3…
2. The gaps are the odd numbers: 3, 5, 7, 9.
✓ 1, 4, 9, 16, 25 … nth term: n²
sequence 2 of 4
Triangular numbers
1. A new row each time: + 2, + 3, + 4, + 5.
2. The gap grows by one each step.
✓ 1, 3, 6, 10, 15 …
sequence 3 of 4
Cube numbers
1. A number times itself, times itself again.
2. 4³ means 4 × 4 × 4, not 4 × 3.
✓ 1, 8, 27, 64, 125 … nth term: n³
1³, 2³, 3³, 4³, 5³ …
sequence 4 of 4
Fibonacci
1. Start 1, 1. Add the last two terms.
2. 1 + 1 = 2, 1 + 2 = 3, 2 + 3 = 5…
✓ 1, 1, 2, 3, 5, 8, 13 …
3 + 5 = 8, then 5 + 8 = 13
know these on sight —
Triangular
1, 3, 6, 10, 15
Fibonacci
1, 1, 2, 3, 5, 8
Spot one hiding inside a question
and the rest gets easier.
The
Maths Habit
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