Sequences

Give the next term in the sequence: 19, 15, 11, 7, 3.

Feb/March 2017

On Monday, Ankuri sent this text message to two friends. "Today is Day Number 1. Tomorrow, please add 1 to the Day Number and send this text message to two friends." Every friend who gets a text message carries out the instructions.

Feb/March 2017

The table lists the first five terms in sequences $A$, $B$ and $C$.

Feb/March 2018

Mrs Verma owns a restaurant. At every table in the restaurant there are 8 chairs. At times, she joins tables together. The diagrams illustrate how the tables are arranged and where each chair (X) is placed. The diagrams show: 1 table with 8 chairs marked X around it. 2 tables joined together with chairs marked around. 3 tables joined together with chairs marked around. A blank space labelled 4 tables. The arrangement of the tables and chairs makes a sequence.

Feb/March 2019

The grid illustrates the first three diagrams in the sequence. Each diagram uses small squares that are either white or grey.

Feb/March 2020

Write down and solve an inequality involving $n$.

Feb/March 2020

The sequence starts with these four terms: 29, 22, 15, 8.

Feb/March 2021

Write down the following two terms.

Feb/March 2021

Find the $n$th term for each sequence given below.

Feb/March 2023

23, 17, 11, 5, ...

Feb/March 2023

State the order of rotational symmetry for the diagram.

Feb/March 2023

Work out the first three terms in this sequence.

Feb/March 2024

Work out the sequence’s first three terms.

Feb/March 2024

The sequence begins with these four terms: 31, 24, 17, 10.

Feb/March 2025

The table presents the first $5$ terms of sequences $A$, $B$ and $C$.

Feb/March 2025

The terms are $2,\ 3,\ 6,\ 11,\ 18,\ \ldots$

May/June 2015

Write down the next two terms for the sequence shown below.

May/June 2015

Find the $n$th term for the sequence $4, 8, 12, 16, 20, \ldots$.

May/June 2015

The sequence runs as follows: 5, 11, 21, 35, 53, ...

May/June 2015

State the next term in this sequence.

May/June 2015

The opening four terms of sequences A, B, C and D are displayed in the table.

May/June 2015

Find the next term in the sequence: 3, 7, 11, 15, …

May/June 2016

The first five terms of a sequence are shown below. 4  11  18  25  32

May/June 2016

The sequence shown is $7, 5, 3, 1, -1, \ldots$

May/June 2016

Find the $n$th term for the sequence $16, 19, 22, 25, 28, \ldots$.

May/June 2016

Write the mathematical name for this solid.

May/June 2016

Every diagram is formed using tiles shaped as equilateral triangles and rhombuses. Each tile has side length 1 unit.

May/June 2016

State the next term in this sequence.

May/June 2017

The diagrams below are constructed from the same rectangles. A dot marks the point where three lines meet, and a cross marks the point where two lines meet.

May/June 2017

Write down the next two terms in the sequence 8, 14, 20, 26, …

May/June 2017

State the first two terms of the sequence.

May/June 2017

The table lists the first four terms of sequences A, B, C and D.

May/June 2017

Write down the first three terms in the sequence.

May/June 2018

The sequence is $a, 13, 9, 3, -5, -15, b, \ldots$.

May/June 2018

Find a rule for the $n$th term of the sequence $11,\;7,\;3,\;-1,\;\ldots$.

May/June 2018

Find the next term in this sequence.

May/June 2018

Marco is creating patterns using grey and white circular mats. Pattern 1, Pattern 2, Pattern 3 and Pattern 4 are illustrated as triangular groups of circles. These patterns make a sequence. Marco then prepares a table to display some information about the patterns.

May/June 2018

The sequence starts with these four terms: 5, 8, 11, 14.

May/June 2019

State the next term in the sequence: 12, 7, 2, -3, -8, ...

May/June 2019

Write down what the next term is.

May/June 2019

The grid displays the first three diagrams in a sequence. Every diagram is built from identical small squares. Each square has side lengths of 1 unit.

May/June 2019

The set of diagrams shown above is formed from tiny lines and dots.

May/June 2019

State the next two terms in the sequence.

May/June 2019

For this sequence, the nth term is $6n-4$.

May/June 2021

The first four members of a sequence are 7, 11, 15, 19.

May/June 2021

Work out the first three terms of this sequence.

May/June 2021

Write down an expression showing the range for $k$ consecutive integers.

May/June 2021

The sequence contains patterns built from rectangular blocks. Pattern 1, Pattern 2, Pattern 3 and Pattern 4 are displayed.

May/June 2021

The table presents four sequences $A, B, C$ and $D$.

May/June 2021

The sequence shown is 22, 17, 12, 7, 2, …

May/June 2022

A sequence has $n$th term given by $n^2 + 12$.

May/June 2022

In this sequence, the $n$th term equals $n^2 - 1$.

May/June 2022

22, 17, 12, 7, 2, ...

May/June 2022

The $n$th term in a sequence is given by $an^2 + bn - 4$. Its first term is $-3$ and its second term is $2$.

May/June 2022

The $n$th term in this sequence is $n^2 + 12$.

May/June 2022

The terms are: 8, 17, 32, 53, 80, ...

May/June 2022

Find the initial three terms of this sequence.

May/June 2022

The diagram depicts a regular polygon.

May/June 2022

Write down the first three terms in this sequence.

May/June 2023

The $n$th term is $10 - n^2$. Write down the first three terms of this sequence.

May/June 2023

The first four terms in the sequence are 2.75, 6, 11.25, 20. Its $n$th term is given by $\frac{1}{4}n^3 + an^2 + bn$.

May/June 2023

State the next term.

May/June 2023

The grid displays the first three diagrams in a sequence, and every diagram is constructed from sticks.

May/June 2023

Calculate the first three terms of this sequence. Write your answers as fractions.

May/June 2023

The table gives some details about two sequences. Sequence A has nth term $60 - 4n$. Sequence B has nth term $n^2 - 300$. The 5th-term column is left blank.

May/June 2024

The sequence starts with these five terms: 11, 18, 25, 32, 39.

May/June 2024

The sequence starts with these four terms: 23, 17, 11, 5.

May/June 2024

State the next term.

May/June 2024

The table gives some details for two sequences.

May/June 2024

The sequence begins with these five terms: 11, 18, 25, 32, 39.

May/June 2024

Find the 4th term for this sequence.

May/June 2024

Write down the rule from one term to the next for this sequence.

May/June 2025

Find the term that comes next in the sequence: 1, 5, 10, 16, 23, …

May/June 2025

The sequence begins with these 4 terms: 11, 8, 5, 2.

May/June 2025

Determine the 10th term of this sequence.

May/June 2025

The table presents three sequences. In Sequence A, the 1st term is 28, the 2nd term is 22, the 3rd term is 16, the 4th term is 10, the 5th term is 4, the 6th term is blank, and the $n$th term is blank. In Sequence B, the 1st term is $1/6$, the 2nd term is $2/7$, the 3rd term is $3/8$, the 4th term is $4/9$, the 5th term is $1/2$, the 6th term is blank, and the $n$th term is blank. In Sequence C, the 1st term is $1/4$, the 2nd term is $1/2$, the 3rd term is $1$, the 4th term is $2$, the 5th term is $4$, the 6th term is blank, and the $n$th term is blank.

May/June 2025

What is the next term in the sequence $5, 9, 13, 17, \ldots$?

Oct/Nov 2015

The sequence shown is $-1, 3, 7, 11, \ldots$.

Oct/Nov 2015

The first four terms of a sequence are 21, 17, 13, 9.

Oct/Nov 2015

Shown here are the first four diagrams in a sequence: Diagram 1, Diagram 2, Diagram 3, Diagram 4, and Diagram 5 are displayed on a grid using the symbols O and X.

Oct/Nov 2015

Below are the first three diagrams in the sequence.

Oct/Nov 2015

Below are the first three diagrams in the sequence. Each diagram is constructed from line segments of length 1 cm.

Oct/Nov 2015

The table lists the first five terms in sequences A, B and C.

Oct/Nov 2015

Find the $n$th term for the sequence $7, 13, 19, 25, 31, \ldots$.

Oct/Nov 2016

Find the $n$th term for the sequence $7, 13, 19, 25, 31, \ldots$

Oct/Nov 2016

The sequence is formed from patterns using lines and dots. The first three patterns in the sequence are displayed. In each pattern, crosses are shown, made from lines with dots arranged around them. The captions beneath the diagrams are: Pattern 1, Pattern 2, Pattern 3, Pattern 4.

Oct/Nov 2016

Fill in the table by stating the next term and the $n$th term for every sequence.

Oct/Nov 2016

Write down the term that comes next.

Oct/Nov 2017

Write down the term that comes next.

Oct/Nov 2017

The first four terms of this sequence are 23, 17, 11, 5.

Oct/Nov 2017

State the first three terms of this sequence.

Oct/Nov 2017

State the next term.

Oct/Nov 2017

The sequence starts with these five terms: $8,\ 11,\ 14,\ 17,\ 20$.

Oct/Nov 2018

Calculate the third term of this sequence.

Oct/Nov 2018

The sequence begins with these five terms: 8, 11, 14, 17, 20.

Oct/Nov 2018

The initial five terms of a sequence are $-4, 2, 8, 14, 20$.

Oct/Nov 2018

The diagram presents the first three patterns in a sequence. They are named Pattern 1, Pattern 2 and Pattern 3, and each is formed from unit squares laid out horizontally with a vertical block underneath. Pattern 4 is not shown.

Oct/Nov 2018

Find the next term and the nth term for the sequence $\frac35,\frac47,\frac59,\frac6{11},\frac7{13},\ldots$.

Oct/Nov 2018

Find the $n$th term for every sequence listed.

Oct/Nov 2019

Write down the term that comes next.

Oct/Nov 2019