Find the next term in each of these sequences.
18, | 21, | 26, | 33, | 42, | ....... |
[1]
18, | 20, | 24, | 32, | 48, | ....... |
[1]
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Syllabus Edition
First teaching 2021
Last exams 2024
Find the next term in each of these sequences.
18, | 21, | 26, | 33, | 42, | ....... |
[1]
18, | 20, | 24, | 32, | 48, | ....... |
[1]
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These are the first four terms of a sequence.
17 | 10 | 3 | -4 |
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Here are the first four terms of a sequence.
32 27 22 17
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Write down the next term in each sequence.
[1]
[1]
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The diagram shows the first three patterns in a sequence.
On the grid, draw pattern 4.
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These are the first four terms of a sequence.
41 35 29 23
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These are the first four terms of a sequence.
29 | 32 | 35 | 38 |
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The th term of a sequence is .
Write down the first three terms of the sequence.
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Find the first three terms of a sequence whose th term is
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Here is a sequence.
Find the value of and the value of .
.................................
.................................
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The nth term of a sequence is
Write down the first three terms of this sequence.
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The th term of a sequence is
Find the first three terms of this sequence.
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The expression for the th term of a sequence is 5.
Work out the third term in this sequence.
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These are the first four terms of a sequence.
-2 | 2 | 6 | 10 |
Find an expression for the th term.
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Find an expression, in terms of , for the th term of this sequence.
....
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These are the first five terms in a sequence.
8 11 14 17 20
Find the next term.
Find an expression for the th term.
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Write down an expression for the nth term of this sequence.
1 8 27 64
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The th term of a sequence is 60-8.
Find the largest number in this sequence.
Here are the first five terms of a different sequence.
12 | 19 | 26 | 33 | 40 |
Find an expression for the th term of this sequence.
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The th term of a sequence is .
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These are the first four terms of a sequence.
27 33 39 45
Find the nth term of this sequence.
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Here are the first three patterns in a sequence.
Pattern | 1 | 2 | 3 | 4 | 5 |
Number of lines | 6 |
[2]
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These are the first four terms of a sequence.
5 | 8 | 11 | 14 |
Write down the next term.
Find an expression, in terms of , for the th term.
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These are the first five terms of a sequence.
-4 2 8 14 20
Find an expression for the th term of this sequence.
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These are the first four terms of a sequence.
8 15 22 29
[1]
[2]
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Here are the first four terms of a sequence.
3 9 15 21
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Find the first three terms of the sequence with th term .
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These are the first four terms of a sequence.
8 | 15 | 22 | 29 |
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The th term of a sequence is
Find the first three terms of this sequence.
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A sequence of patterns is made using black counters and white counters.
Draw Pattern 4.
Complete the table.
Pattern | 1 | 2 | 3 | 4 | 5 |
Number of black counters | 4 | 6 | 8 | ||
Number of white counters | 1 | 4 | 9 |
Write an expression, in terms of , for
Elena has 30 black counters and 140 white counters.
Can she make Pattern 12 using her counters?
Explain your answer.
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Gabriela designs the seating layout for a new theatre.
There are 152 seats in the theatre in total.
Work out the number of rows in the theatre.
......................................... rows
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A road has 349 houses on it numbered from 1 to 349.
The diagram shows some of these houses.
The houses on the West side of the road have odd numbers.
The houses on the East side have even numbers.
Tomaz delivers a leaflet to every house on the West side of the road.
He starts at house number 1 and then delivers to each house in order.
Alicia delivers a leaflet to every house on the East side of the road.
She starts at house number 348 and then delivers to each house in order.
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The grid shows the first three diagrams in a sequence.
Each diagram is made using small squares that are white or grey.
On the grid, draw Diagram 4.
Write down the term to term rule for the number of grey squares.
Diagram number | 1 | 2 | 3 | 4 | ||
Number of small white squares | 1 | 4 | 9 | |||
Number of small grey squares | 3 | 5 | 7 | |||
Total number of small squares | 4 | 9 | 16 |
Complete the table.
Work out the number of small white squares in Diagram 18.
One of the diagrams has a total of 900 small squares.
Work out its Diagram number.
Diagram .................................................
Another diagram has 43 small grey squares.
Work out the total number of small squares in this diagram.
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Here is a sequence of numbers.
3, 6, 11, 18, 27, ...
Find an expression for the nth term of this sequence.
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The grid shows the first three diagrams in a sequence.
Each diagram is made using identical small squares.
Each square has sides that are 1 unit long.
Diagram number | 1 | 2 | 3 | 4 |
Perimeter | 4 | 12 | 20 |
[1]
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These are the first four diagrams in a sequence.
Each diagram is made from small equilateral triangles.
Diagram number () | 1 | 2 | 3 | 4 |
Number of white triangles () | 1 | 3 | 6 | |
Number of grey triangles () | 0 | 3 | ||
Total number of small triangles () | 1 | 4 |
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Mrs Verma has a restaurant.
In the restaurant each table has 8 chairs.
Sometimes she puts tables together.
The diagrams show how the tables are put together and the position of each chair (X).
The pattern of tables and chairs forms a sequence.
Draw the diagram for 4 tables.
Complete the table.
Number of tables (t) | 1 | 2 | 3 | 4 | 5 | 6 |
Number of chairs (c) | 8 | 10 | 12 |
Find a formula for the number of chairs, c, in terms of the number of tables, t.
c = ...............................
18 tables are put together in this way.
Work out the number of chairs needed.
Work out the number of tables, put together in this way, when 80 chairs are needed.
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These are the first four terms of a sequence.
11 15 19 23
[2]
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Each of 196 candidates has a candidate number from 3001 to 3196.
The candidates sit in numerical order in columns and rows, as shown in the diagram.
There are 20 rows.
The diagram shows part of the plan for where the candidates sit.
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A sequence of patterns is made using lines and dots.
The first three patterns in the sequence are shown below.
Draw Pattern 4 on the grid.
Complete the table.
Pattern | 1 | 2 | 3 | 4 | 10 | |
Number of dots | 2 | 3 | ||||
Number of lines | 4 | 7 |
Find an expression, in terms of , for
A pattern has 76 lines.
Work out how many dots are in this pattern.
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