Mathematics·Algebra · NSSCO 6.6
Sequences
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A sequence is a list of numbers that follows a pattern, and once you can read that pattern you gain real power. In this lesson we learn to continue a sequence using its term-to-term rule, then build the nth term of a linear (arithmetic) sequence so we can jump straight to any term at all and even test whether a number belongs. Finally we meet the special sequences — square, cube and triangular numbers, powers and Fibonacci — and learn to tell arithmetic sequences from geometric ones.
What you'll learn in this lesson
By the end you should be able to (NSSCO Mathematics 6.6):
- Recognise patterns in a sequence and continue it, including into negative numbers
- Describe a sequence using its term-to-term rule and its common difference
- Find the nth term of a linear (arithmetic) sequence using nth term = dn + (a − d)
- Use the nth term to find any term, such as the 50th term, in a single step
- Test whether a given number is a member of a sequence using the whole-number check
- Recognise and continue special sequences: square, cube, triangular, powers and Fibonacci
- Distinguish between arithmetic (add/subtract) and geometric (multiply) sequences
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