0606/22 Oct/Nov 2025, Question 8: Geometric Progressions and Sum to Infinity
Cambridge IGCSE Additional Mathematics 0606 · Paper 22 (Calculator) · Calculator · 7 marks
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The question, in short
A sequence with starting value t and step 1.5 has its 4th, 8th and 20th terms forming a geometric sequence; determine t and the geometric ratio.
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Part (a) · 5 marks
Work out the starting value t of the arithmetic sequence using the condition that terms 4, 8 and 20 form a geometric progression.
- 14th, 8th and 20th terms: t + 4.5, t + 10.5, t + 28.5
- 2Geometric: (t + 10.5)/(t + 4.5) = (t + 28.5)/(t + 10.5)
- 3(t + 10.5)² = (t + 4.5)(t + 28.5)
- 4t² + 21t + 110.25 = t² + 33t + 128.25
- 5−12t = 18, so t = −1.5
Answert = −1.5
Part (b) · 2 marks
Using your value of t, calculate the multiplier between consecutive terms of the geometric progression.
- 1Terms of the GP: −1.5 + 4.5 = 3, −1.5 + 10.5 = 9, −1.5 + 28.5 = 27
- 2r = 9/3 = 3
Answer3
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