IB · Mathematics: Applications & Interpretation SL & HL · Number & algebra

Sequences & series: IB Mathematics: Applications & Interpretation questions with answers

Free Sequences & series questions for IB Mathematics: Applications & Interpretation (SL & HL), part of Number & algebra. Each question has the answer and the marking points an examiner would look for.

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Sequences & series practice questions

Question 1Structured · 6 marksA* challenge

A company’s monthly sales of a new product start at 3 thousand units and increase by 20% each month.

(a)

Find the total sales, in thousands, in the first year.

[2]
(b)

Find the least number of months after which total sales exceed 10000 thousand units.

[3]
(c)

Suggest why this model is unlikely to remain valid.

[1]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)119
S12 = 3(1.212 − 1)1.2 − 1 (M1)
119 A1
2
(b)36
3(1.2n − 1)1.2 − 1 > 10000 (M1)
n > 35.7 (A1)
36 A1
3
(c)unbounded growth
sales cannot grow exponentially for ever (market saturates) R1
1
Question 2Structured · 6 marks

The first row of a theatre has 24 seats. Each row after the first has 3 more seats than the row in front of it.

(a)

Find the number of seats in row 12.

[2]
(b)

Find the total number of seats in the first 12 rows.

[2]
(c)

Find the least number of rows needed for the theatre to have at least 1000 seats.

[2]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)57
24 + 11 × 3 (M1)
57 A1
2
(b)486
122(2 × 24 + 11 × 3) (M1)
486 A1
2
(c)20
n2(48 + 3(n − 1)) ≥ 1000 (M1)
20 A1
2
Question 3Structured · 5 marks

The population of a town is 8500 at the start of 2025 and decreases by 2% each year.

(a)

Find the population at the start of 2030.

[2]
(b)

Find the first year in which the population at the start of the year is less than 5950.

[3]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)7683
8500(0.98)5 (M1)
7683 A1
2
(b)2043
8500(0.98)n < 5950 (M1)
n > 17.7 (A1)
2043 A1
3
Question 4Structured · 4 marks

A city’s population of rabbits is 5000 and increases by 5% each year.

(a)

Find the population after 10 years.

[2]
(b)

Find the number of complete years until the population first exceeds double its initial value.

[2]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)8144
un = u1rn (M1)
8144 A1
2
(b)15
equation or GDC table (M1)
15 A1
2
Question 5Structured · 6 marksA* challenge

A company’s monthly sales of a new product start at 5 thousand units and increase by 50% each month.

(a)

Find the total sales, in thousands, in the first year.

[2]
(b)

Find the least number of months after which total sales exceed 5000 thousand units.

[3]
(c)

Suggest why this model is unlikely to remain valid.

[1]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)1287
S12 = 5(1.512 − 1)1.5 − 1 (M1)
1287 A1
2
(b)16
5(1.5n − 1)1.5 − 1 > 5000 (M1)
n > 15.3 (A1)
16 A1
3
(c)unbounded growth
sales cannot grow exponentially for ever (market saturates) R1
1
Question 6Structured · 6 marks

The first row of a theatre has 20 seats. Each row after the first has 3 more seats than the row in front of it.

(a)

Find the number of seats in row 12.

[2]
(b)

Find the total number of seats in the first 12 rows.

[2]
(c)

Find the least number of rows needed for the theatre to have at least 800 seats.

[2]
Show answers and mark scheme
PartAnswer and marking pointsMarks
(a)53
20 + 11 × 3 (M1)
53 A1
2
(b)438
122(2 × 20 + 11 × 3) (M1)
438 A1
2
(c)18
n2(40 + 3(n − 1)) ≥ 800 (M1)
18 A1
2

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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