Free Sequences & series questions for IB Mathematics: Analysis & Approaches (SL & HL), part of Number & algebra. Each question has the answer and the marking points an examiner would look for.
Generate a full Sequences & Series worksheet →All Number & algebra questionsConsider the infinite geometric series 1 + (3x + 45) + (3x + 45)2 + (3x + 45)3 + …
Find the set of values of x for which the series has a finite sum.
The sum to infinity of the series is 43. Find the value of x.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | −3 < x < 13 |3x + 45| < 1 (M1) −5 < 3x + 4 < 5 (A1) −3 < x < 13 A1 | 3 |
| (b) | x = −1112 11 − r = 43 (M1) r = 14 (A1) 3x + 4 = 54 ⇒ x = −1112 A1 | 3 |
The second term of a geometric sequence is −27 and the fifth term is 1.
Find the common ratio.
Find the sum to infinity of the sequence.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | r = −13 u1r = −27, u1r4 = 1 (M1) r3 = −127 (A1) r = −13 A1 | 3 |
| (b) | 2434 u1 = 81 (A1) S∞ = 811 − (−1/3) (M1) 2434 A1 | 3 |
In an arithmetic sequence, u4 = 17 and u9 = 47.
Find the common difference and the first term.
Find the sum of the first 30 terms.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | d = 6, u1 = −1 u1 + 3d = 17, u1 + 8d = 47 (M1) d = 6 A1 u1 = −1 A1 | 3 |
| (b) | 2580 S30 = 302(2(−1) + 29(6)) (M1) 2580 A1 | 2 |
Find the value of Σr=436(r − 7).
| Part | Answer and marking points | Marks |
|---|---|---|
| 429 recognising an arithmetic series with 33 terms (not 36) (M1) first term −3, last term 29 (A1)(A1) 332(−3 + 29) = 429 A1 | 4 |
Offer A: a starting salary of $32000 with an increase of $2000 each year.
Offer B: a starting salary of $32000 with an increase of 4% each year.
Find the salary in year 8 for each offer.
Find the total amount earned over 20 years under each offer.
Find the first year in which the salary under Offer B is greater than the salary under Offer A.
Find the minimum number of complete years after which the total earned under Offer B exceeds the total earned under Offer A.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | A: $46000; B: $42110 A: 32000 + 7(2000) (M1) $46000 A1 B: 32000(1.04)7 (M1) $42110 A1 | 4 |
| (b) | A: $1020000; B: $952899 S20 = 202(2(32000) + 19(2000)) (M1) $1020000 A1 S20 = 32000(1.0420 − 1)1.04 − 1 (M1) $952899 A1 | 4 |
| (c) | year 24 32000(1.04)n−1 > 32000 + (n − 1)(2000) (M1) attempt to solve, e.g. table or graph (M1) year 24 A1 | 3 |
| (d) | 33 years equating or comparing the sums (M1) attempt to solve (M1) 33 A1 | 3 |
A ball is dropped from a height of 2 m. After each bounce it rises to 70% of the height from which it fell.
Find the height reached after the third bounce.
Find the number of bounces after which the ball first rises to less than 0.3 m.
Find the total distance travelled by the ball before it comes to rest.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | 0.686 m 2(0.7)3 (M1) 0.686 m A1 | 2 |
| (b) | 6 2(0.7)n < 0.3 (M1) 6 A1 | 2 |
| (c) | 11.3 m 2 + 2 × 1.401 − 0.7 M1A1 11.3 m A1 | 3 |
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Meet Riyaz →Original IB-style practice questions written for mentorriyaz.in. These are not IB past paper questions, and this site is not affiliated with or endorsed by the International Baccalaureate Organization. Updated 2026-11-04. Paper generator · mentorriyaz.in