The prompt was devised by Helen Hindle, a Lead Practitioner in maths. It generalises from a student's observation made during the intersecting sequences inquiry (see box right). The student proved the statement is true for the sequence generated from 6n + 1. Teachers could use the prompt as the start of a stand-alone inquiry or introduce it as a separate pathway during the intersecting sequences inquiry.
The questions and observations that develop from the statement include:
- Is it true or false?
- If it is true, then is it true for some or all sequences?
- 3 x 5 = 15 and 3, 5 and 15 are in the sequence generated by 2n + 1.
- Does it only work with consecutive terms?
- Are there any sequences when you could use the sum of the terms?
- How could you show this is always true?
- What would happen if you multiplied terms from two sequences? Would the answer be in both sequences?
Students realise that most expressions do not generate arithmetic sequences for which the prompt is true. During exploration, they conclude that the prompt is true for any expression ending with +1. It is also true for any expression in the form an + a, such as 2n + 2, 3n + 3 and so on.