M4.9.7 For the adult
Quadratic sequences
The sequence 2, 6, 12, 20 goes up by more each time. Is there a rule for the nth term?
What this chapter teaches
In a quadratic sequence the second differences are all the same and not 0. The number in front of n² is half the second difference. Take the n² part away from the terms, and what is left is a straight line sequence that gives the rest of the nth term.
Three questions to ask
There is no one right wording. Listen for the idea.
- What are the first and second differences of 2, 6, 12, 20?
- Why is the number in front of n² half the second difference, not the second difference itself?
- How can you check that an nth term is right?
After the chapter, the learner can
- Use second differences to spot a quadratic sequence
- Find the nth term of a sequence like 2, 6, 12, 20
What they copy into their notebook
Find the differences twice. If the second differences match and are not 0, it is quadratic. Halve the second difference for the n² number. Take n² away, then find the rest.