4MA1/1H Jun 2022, Question 23: Sum of an Arithmetic Series
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1H (Higher) · Calculator · 6 marks
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The question, in short
An n-sided polygon (n > 5) has interior angles, largest first, forming an arithmetic sequence starting 177, 175, 173, 171, 169. Find n using algebra.
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Solution · 6 marks
- 1The angles fall by 2: sum of n terms = n/2 × (354 − 2(n − 1)) = n(178 − n)
- 2Interior angles of an n-sided polygon add to (n − 2) × 180
- 3n(178 − n) = 180n − 360, so n² + 2n − 360 = 0
- 4(n − 18)(n + 20) = 0
- 5n > 5, so n = 18
Answer18
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