4PM1/02 Jun 2025, Question 4: Geometric Progressions and Sum to Infinity
Pearson Edexcel International GCSE Further Pure Mathematics 4PM1 · Paper 2 · Calculator · 6 marks
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The question, in short
A geometric series has third term 10 and seventh term 40, with a negative second term. Find the exact common ratio and first term, and explain why no sum to infinity exists.
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Part (a) · 5 marks
Find (i) the exact value of r and (ii) the value of a, given the second term is negative.
- 1ar⁶/ar² = 40/10, so r⁴ = 4
- 2r = ±√2
- 3The second term ar is negative and a = 10/r² > 0, so r = −√2
- 4ar² = 10, so a = 10/2 = 5
Answer(i) r = −√2 (ii) a = 5
Part (b) · 1 mark
Explain why the series G has no sum to infinity.
- 1|r| = √2 > 1
- 2So the series does not converge and has no sum to infinity
Answer|r| = √2 > 1, so the series is not convergent
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