4MA1/2HR Jun 2019, Question 17: Pattern Sequences and Special Sequences
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 2HR (Higher) · Calculator · 4 marks
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The question, in short
Using the table of the first six terms written as products divided by 2, prove algebraically that adding any two consecutive terms always gives a square number.
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Solution · 4 marks
- 1Term n = 1/2 n(n+1)
- 2Term n+1 = 1/2 (n+1)(n+2)
- 3Sum = 1/2 n(n+1) + 1/2 (n+1)(n+2)
- 4Factor out 1/2 (n+1): 1/2 (n+1)(n + n+2)
- 5Simplify: 1/2 (n+1)(2n+2)
- 6Factor 2: 1/2 (n+1) * 2(n+1) = (n+1)²
Answer(n + 1)²
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