What you need to know
This area combines pattern recognition with algebra and graphical interpretation. Learn to move between a sequence rule, a function rule, a table and a graph without losing the meaning of the variables.
- Find and use nth-term rules for common sequences.
- Evaluate functions by substituting inputs carefully.
- Interpret gradient, intercepts and intersections from graphs.
- Link graphs with equations and real-world relationships.
Key mathematics
Linear sequence nth term
u_n=a+(n-1)d
Useful when the sequence has a constant difference.Function notation
y=f(x)
x is the input and f(x) is the output.Worked example
For the sequence $5,8,11,14,\dots$, the common difference is 3. The nth term is $$u_n=5+3(n-1)=3n+2.$$ Therefore the 20th term is 62.
EXAM TECHNIQUE
Exam tips
- Use a table of differences when the nth term is not immediately obvious.
- Substitute negative inputs into functions using brackets.
- On graphs, read the scale on both axes before taking coordinates.
WATCH OUT
Common mistakes
- Using n instead of n minus 1 in a sequence formula.
- Forgetting brackets when substituting a negative value for x.
- Reading graph coordinates from grid squares without checking the axis scale.
Frequently asked questions
How do I find an nth term?
Start by checking whether the first differences are constant; if they are, use a linear nth-term pattern.
What is function notation?
It is a compact way to describe the output produced by a rule for a given input.
Why do graph intersections matter?
An intersection gives values that satisfy both plotted relationships at the same time.