Free Arithmetic & geometric progressions questions for IGCSE Additional Mathematics (0606), part of Series & counting. Each question has the answer and the marking points an examiner would look for.
Generate a full Arithmetic & Geometric Progressions worksheet →All Series & counting questionsThe second term of a geometric progression is 18 and the fifth term is 163. Find the first term, the common ratio and the sum to infinity.
| Part | Answer and marking points | Marks |
|---|---|---|
| a = 27, r = ⅔, S∞ = 81 r3 = 163 ÷ 18 = 827 M1 r = ⅔ A1 a = 27 A1 S∞ = 81 A1 | 4 |
The first term of a geometric progression is 81 and the common ratio is 23.
Find the sum to infinity.
Find the least number of terms whose sum exceeds 99% of the sum to infinity.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | 243 a ÷ (1 − r) M1 243 A1 | 2 |
| (b) | 12 1 − rn > 0.99 M1 logs M1 12 A1 | 3 |
The first term of an arithmetic progression is 12 and the common difference is 5.
Find the 30th term.
Find the sum of the first 30 terms.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | 157 157 B1 | 1 |
| (b) | 2535 S = n2(2a + (n − 1)d) M1 2535 A1 | 2 |
The first term of a geometric progression is 81 and the common ratio is 13.
Find the sum to infinity.
Find the least number of terms whose sum exceeds 99% of the sum to infinity.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | 121.5 a ÷ (1 − r) M1 121.5 A1 | 2 |
| (b) | 5 1 − rn > 0.99 M1 logs M1 5 A1 | 3 |
The 3rd term of an arithmetic progression is 15 and the 10th term is 50. Find the first term, the common difference and the sum of the first 20 terms.
A geometric progression has first term 57 and common ratio 0.2. Find the sum to infinity.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | a = 5, d = 5, S20 = 1050 Two equations formed M1 d = 5 A1 a = 5 A1 S20 = 1050 A1 | 4 |
| (b) | 71.3 a ÷ (1 − r) M1 71.3 A1 | 2 |
The first term of an arithmetic progression is 9 and the common difference is 4.
Find the 25th term.
Find the sum of the first 25 terms.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | 105 105 B1 | 1 |
| (b) | 1425 S = n2(2a + (n − 1)d) M1 1425 A1 | 2 |
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Meet Riyaz →Original Cambridge-style practice questions written for mentorriyaz.in. These are not Cambridge past paper questions, and this site is not affiliated with or endorsed by Cambridge University Press & Assessment. Updated 2026-11-04. Paper generator · mentorriyaz.in