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4024/21 Oct/Nov 2023, Question 4: Quadratic and Cubic Sequences

Cambridge O Level Mathematics 4024 · Paper 21 (Calculator) · Calculator · 11 marks

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The question, in short

Work with two sequences: one given by its first five terms, and another defined by a quadratic nth-term formula involving constants a and b.

Summarised in our own words. Use the official paper for the exact wording and any diagrams.

Part (ai) · 1 mark

Continue the given list of five numbers and state the following term.

  1. 1Add 7 each time: 33 + 7 = 40

Answer40

Part (aii) · 2 marks

Write a formula in terms of n that produces the given sequence.

  1. 1Common difference 7, so 7n + j
  2. 2First term: 7 × 1 + j = 5 so j = −2
  3. 3nth term = 7n − 2

Answer7n−2

Part (aiii) · 3 marks

Two consecutive terms Tₖ and Tₖ₊₁ add to 703; determine k.

  1. 1(7k − 2) + (7(k + 1) − 2) = 703
  2. 214k + 3 = 703
  3. 314k = 700 so k = 50

Answer50

Part (b) · 5 marks

Given the 1st term is 3 and the 3rd term is 19 for n² + an + b, work out the 6th term.

  1. 1n = 1: 1 + a + b = 3 so a + b = 2
  2. 2n = 3: 9 + 3a + b = 19 so 3a + b = 10
  3. 3Subtract: 2a = 8 so a = 4, b = −2
  4. 46th term = 6² + 4 × 6 − 2 = 36 + 24 − 2 = 58

Answer58

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Also searched as: 4024/21/O/N/23 · 4024_w23_qp_21 · 4024 w23 21 · question 4.
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