Sequences

Calculate 7² × 2³.

Write down the next two numbers in the following sequence.

Write the next term in the sequence below.

Draw Diagram 1 in the sequence below.

Diagram 1 Diagram 2 Diagram 3 Diagram 4

The sequence of numbers shown below is linear.

Two of the numbers are missing.

Fill in the missing numbers in the sequence.

Write down the rule for finding the next term in the sequence.

Calculate 7² × 2³.

Calculate 0∙04 × 0∙9.

Calculate 11% of 8400.

Write down the next two numbers in the following sequence.

Write down the next number in this sequence.

Write down the next two numbers in this sequence.

40 000, 20 000, 10 000, 5000,_{........ ……},_{........ ……}

The n th term of a sequence is given by 5 n − 1.

Calculate the sum of the first three terms.

You must show all your working.

Ben thinks of a number sequence.

The difference between each term and the next is the same.

The first term in the sequence is 11. The fourth term in the sequence is 23.

What are the values of the second and third terms in Ben’s sequence?

Write down the next term in each of the sequences below.

53, 80, 107, 134,_........

24, 72, 216, 648,_........

Write down the next two numbers in the following sequence.

Simplify the expression 5y + 7m − 3y −10m.

Write down the next two numbers in the following sequence.

f 3g 2h.

Calculate the value of f when g = 9·3 and h = −13·6.

Write down the next number in each of the following sequences.

67, 73, 79, 85,_........

103, 92, 81, 70,_........

Simplify 3a 2a a.

How many dots will there be in Diagram 6?

Describe in words the rule for continuing the sequence below.

79, 65, 51, 37,... Rule:

Write down the next term in the sequence below.

Adrian has n grapes. He eats 4 of them.

Write down, in terms of n, the total number of grapes Adrian now has.

Write the next term in the sequence below.

Describe the rule for continuing the following sequence.

77, 64, 51, 38, 25,...

Rule:

A dog is x years old. Another dog is 2 years younger.

Write down, in terms of x, the age of the younger dog.

Write down the next number in each of the following sequences.

29, 35, 41, 47, …………

2000, 1000, 500, 250, …………

Write down the next two numbers in the following sequence.

Use the formula x = 4a + 3b to find the value of x when a = 7·2 and b = − 4·6.

Write an expression for the n th term of the following sequence.

The first four diagrams in a sequence are shown below.

Diagram 1 Diagram 2 Diagram 3
Diagram 4

Complete the following subtraction.

The first three diagrams in another sequence are shown below.

Give an expression, in terms of n, for the number of dots (●) in Diagram n.

You must simplify your expression.

Write down the next two numbers in the following sequence.

Use the formula x = 4a + 3b to find the value of x when a = 7·2 and b = − 4·6.

Write an expression for the n th term of the following sequence.

The first four diagrams in a sequence are shown below.

Diagram 1 Diagram 2 Diagram 3
Diagram 4

Complete the following subtraction.

The first three diagrams in another sequence are shown below.

Give an expression, in terms of n, for the number of dots (●) in Diagram n.

You must simplify your expression.

Fill in the missing term in each of these number sequences.

100, 91,_{…........ ………}, 73, 64

4,_{…........ ………}, 18, 25, 32

Write down the next two numbers in the following sequence.

−19 −15 −11 −7 ……. ………

Rods are used to make a sequence of patterns as shown below.

Pattern 1 uses six rods.

How many rods are required to draw Pattern 4?

Pattern 37 requires 186 rods.

How many rods are required to draw Pattern 38?

Describe in words the rule used in the following sequence.

243 81 27 9 …….

Describe in words the rule for continuing each of the following sequences.

38, 32, 26, 20, …

Rule:

Rule:

Adam has x marbles. His friend gives him 3 more.

Write down, in terms of x, the total number of marbles Adam now has.

Petrol costs £g per litre.

Write down, in terms of g, the cost of 15 litres of petrol.

Write down the next two numbers in the following sequence.

−19 −15 −11 −7 ……. ………

Rods are used to make a sequence of patterns as shown below.

Pattern 1 uses six rods.

How many rods are required to draw Pattern 4?

Pattern 37 requires 186 rods.

How many rods are required to draw Pattern 38?

Describe in words the rule used in the following sequence.

243 81 27 9 …….

One of the values below is the solution to k + 3 = 6·9

Circle the correct answer.

2·3 20·7 3·9 9·9 207

Simplify the expression 12w + 15w – w.

Write down the next term in the following sequence.

Describe in words the rule for continuing the following sequence.

4, 12, 36, 108, …

Look at the sequence:

8, 16, 24, 32, …

Will any of the first 100 terms of this sequence be a prime number?

Explain how you know.

Describe the rule for continuing each of the following sequences.

27, 32, 37, 42, 47,...

Rule:

6, 12, 24, 48, 96,...

Rule:

Write the next term in the sequence below.

....

The table below shows the first five terms of a sequence of numbers.

Circle the correct equation that connects terms t₆ and t₇.

The nth term of another sequence is given by 2n – 11.

Write down the value of,

the 10th term,

the 3rd term.

Write down the next two numbers in the following sequence.

Expand 5(3x – 2).

Solve 9x + 3 = 4x + 5.

Write down the next two numbers in the following sequence.

Find the value of 2x + 7y when x = –3 and y = 10.

Write down the next two numbers in the following sequence.

Find the value of 2x + 7y when x = –3 and y = 10.

Simplify the expression 8k + 3m – 2k – 8m.