Chapter 10: Review

The chapter problem, solved

Pattern A starts at $5$ and adds $3$ tiles each design. Its nth term is $3n+2$. Pattern B starts at $2$ and doubles each design. Its term at position $n$ is $2^n$.

Compare the totals:

Pattern B first has more tiles at design $4$. For design $5$, Pattern A has $17$ tiles and Pattern B has $32$.

Mixed practice: choose a method and explain why

For each question, name the type of rule or calculation you will use before working it out.

1. Continue the sequence $3,8,13,18,\ldots$ by two terms.
2. Find the 20th term of the sequence with nth term $5n-2$.
3. Is $64$ a square number, a cube number, both, or neither?
4. Write the next two triangular numbers after $15$.
5. Find the nth term of $9,13,17,21,\ldots$.
6. Find the nth term of $1,4,9,16,25,\ldots$.
7. Continue $2,6,18,54,\ldots$ by one term.
8. Work out $0.75$ of $240$.
9. Solve $4x+7=31$.
10. A sequence begins $12,7,2,-3,\ldots$. State its common difference and find its 10th term.

What you can now do

• describe and continue sequences from their rules;
• recognise square, cube, triangular, and Fibonacci sequences;
• find linear, quadratic, and geometric rules;
• choose a method and check whether it fits the terms.

Return to your connection

Return to the pattern you described at the chapter start. Can you write a rule for it now? Explain what the position number would mean in your example.