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Sequences and the nth term
A sequence follows a rule. Finding the nth term lets you jump straight to any term without counting.
Linear sequences
The terms go up or down by the same amount each time: the common difference.
5, 8, 11, 14, ... has a difference of 3.
5, 8, 11, 14, ... has a difference of 3.
Finding the nth term
nth term = (difference) × n + (adjustment)
5, 8, 11, 14: difference 3, so start with 3n: 3, 6, 9, 12. Add 2 to match.
nth term = 3n + 2
5, 8, 11, 14: difference 3, so start with 3n: 3, 6, 9, 12. Add 2 to match.
nth term = 3n + 2
Other sequences
Square numbers: 1, 4, 9, 16 (n2).
Fibonacci-type: add the two previous terms: 1, 1, 2, 3, 5, 8.
Geometric: multiply by the same number: 3, 6, 12, 24 (× 2).
Fibonacci-type: add the two previous terms: 1, 1, 2, 3, 5, 8.
Geometric: multiply by the same number: 3, 6, 12, 24 (× 2).
Is 100 a term in the sequence 3n + 2?
- Set 3n + 2 = 100
- 3n = 98
- n = 32.67, which is not a whole number
Answer: No
For a linear sequence, the nth term is (difference)n + (adjustment). Check by putting n = 1. A number is in the sequence only if n comes out whole.
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