4MA1/1H Jan 2023, Question 22: Sum of an Arithmetic Series
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1H (Higher) · Calculator · 4 marks
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The question, in short
Arithmetic series has first term 2t+1, nth term 14t−5, common difference 3. Express the sum of the first n terms as p(qt−1)ʳ and find integers p, q, r, showing working.
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Solution · 4 marks
- 1nth term: (2t + 1) + 3(n − 1) = 14t − 5, so 3n = 12t − 3 and n = 4t − 1
- 2Sum = n/2 × (first term + last term) = (4t − 1)/2 × (2t + 1 + 14t − 5)
- 3= (4t − 1)/2 × (16t − 4) = (4t − 1)/2 × 4(4t − 1)
- 4= 2(4t − 1)², so p = 2, q = 4, r = 2
Answerp = 2, q = 4, r = 2
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