WMA12/01 Jan 2025, Question 4: Geometric Progressions and Sum to Infinity
Pearson Edexcel International AS Level Mathematics · Pure Mathematics 2 (WMA12) · Calculator · 6 marks
The question, in short
A geometric series has first three terms summing to 70.2 and sum to infinity 75; find its common ratio and first term, showing full working without relying on calculator methods.
Summarised in our own words. Use the official paper for the exact wording and any diagrams.
Part (a) · 4 marks
Find the common ratio of the geometric series using the given sum of first three terms and sum to infinity.
- 1a(1 − r³)/(1 − r) = 70.2 and a/(1 − r) = 75
- 2Substitute the second into the first: 75(1 − r³) = 70.2
- 31 − r³ = 0.936, so r³ = 0.064
- 4r = 0.4
Answerr = 0.4
Part (b) · 2 marks
Find the first term of the geometric series.
- 1a/(1 − 0.4) = 75
- 2a = 75 × 0.6
- 3a = 45
Answera = 45
Stuck on a step? Read the free lesson: Geometric Progressions and Sum to Infinity
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