Sequences

Here are the first four terms of a number sequence.

7 11 15 19

Write down the next term of the sequence.

Explain how you found your answer to part (a)

Find the 12th term of the sequence.

Here are the first four terms of a number sequence.

5 12 19 26

Write down the next term of the sequence.

Explain how you worked out your answer.

Simplify c + c + c + c + c

Simplify 7w + 10y ‒ 9w + 2y

The nth term of a sequence is given by 7n – 4

Find the 1st term and the 5th term of the sequence.

Solve 7(x + 5) = 8 ‒ 3x Show clear algebraic working.

Here are the first five terms of a number sequence.

−3 5 13 21 29

Write down the next term of the sequence.

Explain how you worked out your answer.

Explain why 326 cannot be a term of the sequence.

Here are the first four terms of a number sequence.

2 6 10 14

Elsie correctly works out that the next term in the sequence is 18

Explain how she was able to work this out.

Explain why 217 cannot be a number in the sequence.

Here is a sequence of patterns made from sticks.

Pattern number 1 Pattern number 2 Pattern number 3

In the space below, draw Pattern number 4

Complete the table.

Work out the number of sticks in Pattern number 10

Connor says that in Pattern number 25 there are 102 sticks.

Explain why Connor is wrong.

A sequence of patterns is made from squares.

Pattern number 1
Pattern number 2
Pattern number 3

Complete the table.

Work out the number of squares in Pattern number 8

Angus says

“there are 42 squares in Pattern number 15”

Angus is incorrect.

Explain why.

Here are the first five terms of a number sequence.

4 10 16 22 28

Write down the next term of the sequence.

Explain how you worked out your answer.

Work out the 13th term of the sequence.

Explain why 467 cannot be a number in the sequence.

Here are the first five terms of a number sequence.

1 7 13 19 25

Write down the next term of the sequence.

Explain how you worked out your answer.

Explain why 188 cannot be a number in the sequence.

Here are the first 4 terms of a number sequence.

7 12 17 22

Write down the next term of the sequence.

Explain how you worked out your answer.

Is 256 a number in the sequence?

Tick one of the boxes below and give a reason for your answer.

Give a reason for your answer.

The table shows the temperatures recorded at midnight and at midday for each of five North American cities on a Monday one week.

Which city had the lowest midnight temperature?

Find the difference between the midnight temperature and midday temperature for Boston.

From Monday to Thursday, the midday temperature in Detroit increased by 2°C each day.

Work out the midday temperature in Detroit on Thursday.

A sequence of shapes is made by shading squares on a square grid.

On the grid, draw Shape number 4

Complete the table.

Find the number of shaded squares in Shape number 8

Explain why no shape in the sequence is made by shading exactly 50 squares.

Here are the first five terms of a number sequence.

1 3 9 27 81

Find the next term of this sequence.

Explain how you found this term.

The 9th term of this number sequence is 6561

Find the 10th term of this sequence.

Here are the first five terms of a number sequence.

3 7 11 15 19

Write down the next term of the sequence.

Explain how you worked out your answer.

Find the first number greater than 70 that is in the sequence.

Ada says, “96 is a number in the sequence”

Is Ada correct? You must give a reason for your answer.

Here is a sequence of patterns made from square tiles.

Pattern number 1
Pattern number 2
Pattern number 3

In the space below, draw Pattern number 4

Complete the table.

Work out the number of tiles in Pattern number 30

Liz says that in Pattern number n, the number of tiles is 2n.

Is Liz correct? You must give a reason for your answer.

Here is a sequence of patterns made from circles.

number 1
number 2
number 3
number 4

In the space below, draw Pattern number 5

Complete the table.

Work out the number of circles in Pattern number 8

C is the number of circles in Pattern number P

Write down a formula for C in terms of P

A different sequence of patterns is made from triangles. The rule to find the number of triangles in each pattern is

multiply the Pattern number by 5 and subtract 4

Is there a pattern in this sequence that is made from exactly 136 triangles? You must give a reason for your answer.