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Write down the missing values in the table shown.
| Stage number (n) | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| Number of blocks (C) | 4 | 7 | 10 | 13 |
Marking key
- 16 and 19
Expected answer
C when n = 5: 16
C when n = 6: 19
Worked solution
C goes 4, 7, 10, 13 – up by 3 each stage.
13 + 3 = 16
16 + 3 = 19
→ Stage 5: C = 16, Stage 6: C = 19
Three arms each gain one block per stage, so C rises by 3 every time.
Write down, in simplest form, a general rule for C in terms of n.
Marking key
- C = 3n + 1 (A1 for 3n, A1 for + 1; accept 1 + 3n)
Worked solution
Common difference 3, so the rule starts 3n. Test n = 1: 3(1) = 3, but C = 4, so add 1.
Check n = 4: 3(4) + 1 = 13 ✓
Each stage adds one block to each of the three arms; the centre block is the + 1.
Solve = 5
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