4024/12 May/Jun 2020, Question 17: Pattern Sequences and Special Sequences
Cambridge O Level Mathematics 4024 · Paper 12 (Non-calculator) · Non-calculator · 4 marks
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The question, in short
A sequence is given by T₁ = 1² + 3 = 4, T₂ = 2² + 8 = 12, T₃ = 3² + 13 = 22, T₄ = 4² + 18 = 34. Find T₅ and a formula for Tₙ.
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Part (a) · 1 mark
Work out the value of the fifth term, T₅, of the sequence.
- 1T₅ = 5² + 23 = 25 + 23 = 48
Answer48
Part (b) · 3 marks
Find an expression in terms of n that gives the nth term Tₙ.
- 1Each term is n² plus an extra number: 3, 8, 13, 18.
- 2The extras go up by 5 each time, so they are 5n + k.
- 3When n = 1: 5 + k = 3, so k = −2.
- 4Tₙ = n² + 5n − 2
Answern² + 5n − 2
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