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SL 1.3—Geometric Sequences - IB Questionbank | RevisionDojo

Practice SL 1.3—Geometric Sequences with authentic IB Mathematics Applications & Interpretation (AI) exam questions for both SL and HL students. This question bank mirrors Paper 1, 2, 3 structure, covering key topics like core principles, advanced applications, and practical problem-solving. Get instant solutions, detailed explanations, and build exam confidence with questions in the style of IB examiners.

Paper

Level

Question 1

HLPaper 2

It is known that the number of fish in a certain pond will decrease by $7\%$ each year unless some new fish are added. At the end of each year, 250 new fish are added to the pond.

At the start of 2018, there are 2500 fish in the pond.

Show that there will be approximately 2645 fish in the pond at the start of 2020.

Find the approximate number of fish in the pond at the start of 2042.

Question 2

SLPaper 2

Rosa joins a club to prepare to run a marathon. During the first training session Rosa runs a distance of 3000 metres. Each training session she increases the distance she runs by 400 metres.

A marathon is 42.195 kilometres.

In the $k$ th training session Rosa will run further than a marathon for the first time.

Carlos joins the club to lose weight. He runs 7500 metres during the first month. The distance he runs increases by 20% each month.

Write down the distance Rosa runs in the third training session.

[1]

Find the value of $k$ .

[2]

Calculate the total distance, in kilometres, Rosa runs in the first 50 training sessions.

[4]

Calculate the total distance Carlos runs in the first year.

[3]

Find the distance Carlos runs in the fifth month of training.

[3]

Write down the distance Rosa runs in the $n$ th training session.

[2]

Question 3

SLPaper 2

A car depreciates in value exponentially. The initial value of the car is $20,000, and it depreciates at a rate of 15% per year.

Calculate the value of the car after 5 years.

[2]

Determine the time it takes for the car's value to halve.

[2]

Question 4

HLPaper 2

Consider a geometric sequence with a first term of 4 and a fourth term of −2.916.

Find the sum to infinity of this sequence.

Find the common ratio of this sequence.

Question 5

SLPaper 2

A renewable energy company is analyzing the output of a solar panel system that produces energy in a geometric sequence. The initial output is 10 kWh, and it doubles every hour.

Write down the first term $u_1$ and the common ratio $r$ .

[1]

Find the output after 10 hours.

[2]

Express the general term $u_n$ in terms of $n$ .

[1]

Find the value of n given that $u_n = 20480$ kWh.

[2]

Question 6

SLPaper 2

A technology company has a product that starts at a price of $2 and increases by 5% each year.

Find the value of the smallest price that exceeds $500.

[6]

Question 7

SLPaper 2

A company is reducing its production of a certain product, starting with an output of 10 units, and halving the production every hour.

Write down the first term $u_1$ and the common ratio $r$ .

[1]

Find the output after 10 hours.

[2]

Calculate the total production in the first 10 hours.

[2]

Express the general term $u_n$ in terms of $n$ .

First four terms: $u_1 = 3$ $u_2 = 7$ $u_3 = 11$ $u_4 = 15$

[1]

Find the value of n given that $u_n = 0.3125$ units.

[2]

Question 8

SLPaper 2

The first terms of an infinite geometric sequence, ${u_n}$ , are 2, 6, 18, 54, …

The first terms of a second infinite geometric sequence, ${v_n}$ , are2, −6, 18, −54, …

The terms of a third sequence, ${w_n}$ , are defined as ${w_n} = {u_n} + {v_n}$ .

The finite series, $\sum\limits_{k = 1}^{225} {{w_k}}$ ,can also be written in the form $\sum\limits_{k = 0}^m {4{r^k}}$ .

Write down the first three non-zero terms of ${w_n}$ .

[3]

Find the valueof $r$ .

[2]

Find the valueof $m$ .

[2]

Question 9

SLPaper 2

The first term of an infinite geometric sequence is 4. The sum of the infinite sequence is 200.

Find the common ratio.

[2]

Find the sum of the first 8 terms.

[2]

Find the least value of n for which S_n > 163.

[3]

Question 10

HLPaper 1

The geometric sequence u₁, u₂, u₃, … has common ratio r.

Consider the sequence $A = \left\{ {{a_n} = {\text{lo}}{{\text{g}}_2}\left| {{u_n}} \right|{\text{:}}\,n \in {\mathbb{Z}^ + }} \right\}$ .

Show that A is an arithmetic sequence, stating its common difference d in terms of r.

[4]

A particular geometric sequence has u₁ = 3 and a sum to infinity of 4.

Find the value of d.

[3]

SL 1.3—Geometric Sequences Questionbank