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Geometric sequences - MYP Questionbank | RevisionDojo

Practice Geometric sequences with authentic MYP MYP Extended Mathematics 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 MYP examiners.

Type

Difficulty

Question 1

True or False: A sequence where every term is $7$ ( $7, 7, 7, 7, \dots$ ) is geometric with a common ratio $r = 1$ .

Question 2

For the geometric sequence $u_n = 200(0.5)^{n-1}$ , what is the smallest integer $n$ such that $u_n < 1$ ?

Question 3

In a geometric sequence, $u_2 = 10$ and $u_3 = 5$ . Find the value of the first term, $u_1$ .

Question 4

Consider a geometric sequence $u_1, u_2, u_3, \dots$ where the first term $u_1$ is positive. The sequence satisfies the property that every term is strictly less than the term two places before it, such that:

u_{n+2} < u_n \quad \text{for all } n \ge 1

Which of the following describes all possible values for the common ratio $r$ ?

Question 5

If $x$ , $15$ , and $x+16$ are three consecutive terms of a geometric sequence with a common ratio $r > 0$ , determine the value of $x$ .

Question 6

A geometric sequence $u_1, u_2, u_3, \dots$ has a common ratio $r$ .

Which of the following describes the sequence of squares $u_1^2, u_2^2, u_3^2, \dots$ ?

Question 7

A sequence is given by $u_n = 3 \times (0.8)^{n-1}$ . What happens to the terms of the sequence as $n$ becomes very large?

Question 8

A geometric sequence is defined by $u_1 = k$ and $u_3 = 4k$ , where $k \neq 0$ . What are the possible values for the common ratio $r$ ?

Question 9

A geometric sequence has $u_1 = 100$ . Each subsequent term is $10\%$ smaller than the previous term. The value of $u_5$ is ____.

Question 10

A geometric sequence has a first term $u_1 = 5$ and a common ratio $r = 3$ . Which of the following expressions correctly represents the $n^{\text{th}}$ term $u_n$ ?

Type

Difficulty

Question 1

True or False: A sequence where every term is $7$ ( $7, 7, 7, 7, \dots$ ) is geometric with a common ratio $r = 1$ .

Question 2

For the geometric sequence $u_n = 200(0.5)^{n-1}$ , what is the smallest integer $n$ such that $u_n < 1$ ?

Question 3

In a geometric sequence, $u_2 = 10$ and $u_3 = 5$ . Find the value of the first term, $u_1$ .

Question 4

u_{n+2} < u_n \quad \text{for all } n \ge 1

Which of the following describes all possible values for the common ratio $r$ ?

Question 5

If $x$ , $15$ , and $x+16$ are three consecutive terms of a geometric sequence with a common ratio $r > 0$ , determine the value of $x$ .

Question 6

A geometric sequence $u_1, u_2, u_3, \dots$ has a common ratio $r$ .

Which of the following describes the sequence of squares $u_1^2, u_2^2, u_3^2, \dots$ ?

Question 7

A sequence is given by $u_n = 3 \times (0.8)^{n-1}$ . What happens to the terms of the sequence as $n$ becomes very large?

Question 8

A geometric sequence is defined by $u_1 = k$ and $u_3 = 4k$ , where $k \neq 0$ . What are the possible values for the common ratio $r$ ?

Question 9

A geometric sequence has $u_1 = 100$ . Each subsequent term is $10\%$ smaller than the previous term. The value of $u_5$ is ____.

Question 10

A geometric sequence has a first term $u_1 = 5$ and a common ratio $r = 3$ . Which of the following expressions correctly represents the $n^{\text{th}}$ term $u_n$ ?

Type

Difficulty

Question 1

True or False: A sequence where every term is $7$ ( $7, 7, 7, 7, \dots$ ) is geometric with a common ratio $r = 1$ .

Question 2

For the geometric sequence $u_n = 200(0.5)^{n-1}$ , what is the smallest integer $n$ such that $u_n < 1$ ?

Question 3

In a geometric sequence, $u_2 = 10$ and $u_3 = 5$ . Find the value of the first term, $u_1$ .

Question 4

u_{n+2} < u_n \quad \text{for all } n \ge 1

Which of the following describes all possible values for the common ratio $r$ ?

Question 5

If $x$ , $15$ , and $x+16$ are three consecutive terms of a geometric sequence with a common ratio $r > 0$ , determine the value of $x$ .

Question 6

A geometric sequence $u_1, u_2, u_3, \dots$ has a common ratio $r$ .

Which of the following describes the sequence of squares $u_1^2, u_2^2, u_3^2, \dots$ ?

Question 7

A sequence is given by $u_n = 3 \times (0.8)^{n-1}$ . What happens to the terms of the sequence as $n$ becomes very large?

Question 8

A geometric sequence is defined by $u_1 = k$ and $u_3 = 4k$ , where $k \neq 0$ . What are the possible values for the common ratio $r$ ?

Question 9

A geometric sequence has $u_1 = 100$ . Each subsequent term is $10\%$ smaller than the previous term. The value of $u_5$ is ____.

Question 10

A geometric sequence has a first term $u_1 = 5$ and a common ratio $r = 3$ . Which of the following expressions correctly represents the $n^{\text{th}}$ term $u_n$ ?

Geometric sequences Questionbank