4024/22 Oct/Nov 2021, Question 4: The nth Term of a Linear Sequence
Cambridge O Level Mathematics 4024 · Paper 22 (Calculator) · Calculator · 9 marks
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The question, in short
Work with a counter pattern sequence shown in a diagram, complete a table, derive a formula in n, and solve a linear sequence problem.
Summarised in our own words. Use the official paper for the exact wording and any diagrams.
Part (ai) · 1 mark
Fill in the missing counter totals for patterns 4 and 5 in the table.
- 1Add 4 each time: Pattern 4 = 20, Pattern 5 = 24
Answer| Pattern number | 4 | 5 | | Number of counters | 20 | 24 |
Part (aii) · 2 marks
Write an expression in n giving the counter count for pattern n.
- 1Count the counters: 8, 12, 16 in Patterns 1, 2, 3
- 2They go up by 4 each time, so the rule is 4n + k
- 3Pattern 1: 4 × 1 + k = 8, so k = 4
- 4Counters in Pattern n = 4n + 4
Answer4n + 4
Part (aiii) · 2 marks
With 150 counters, determine the largest pattern number p that can be built.
- 14p + 4 ≤ 150 → 4p ≤ 146 → p ≤ 36.5
- 2p = 36
Answer36
Part (bi) · 2 marks
A linear sequence has 4th term 26 and 8th term 2; find its first term.
- 1Difference = (2 − 26)/(8 − 4) = −24/4 = −6
- 2First term = 26 − 3 × (−6) = 26 + 18 = 44
Answer44
Part (bii) · 2 marks
Give an expression in n for the nth term of that linear sequence.
- 1nth term = 44 − 6(n − 1)
- 2= 50 − 6n
Answer50 − 6n
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Also searched as: 4024/22/O/N/21 · 4024_w21_qp_22 · 4024 w21 22 · question 4.
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