When the differences change by the same amount each time, the nth term has an n² term. Find it.
What you will learn
- Continue a quadratic sequence using second differences
- Find the nth term an² + bn + c
- Use a quadratic nth term
Second differences
- 4, 9, 16, 25, 36, ...
- first differences: 5, 7, 9, 11
- second difference: 2
A constant second difference means a quadratic sequence. The n² coefficient is half the second difference.
The rest of this lesson and its 7 practice questions are locked.
In this lesson
- Second differences
- The nth term in three steps
7 practice questions, marked as you go; about 25 minutes in all.
Key terms
Half
In this unit: Sequences
Term-to-term rules, the nth term of linear sequences, special sequences, geometric sequences and (Higher) the nth term of quadratic sequences.