Welcome to our lighthearted maths quiz on sequences! Don't worry, we're not talking about lengthy film sequences, but interesting numerical patterns. This quiz is designed specifically for Key Stage 3 students to test your understanding of mathematical sequences. So grab your thinking caps, flex your number-crunching muscles and let's explore the fascinating world of sequences together in this 10-question challenge. Good luck!

1.

How do you find the nth term of an arithmetic sequence where the first term is 3 and the common difference is 2?

3n + 2

2n + 3

3n - 2

2n - 3

2 is the common difference and 3 is the first term, so 2n + 3 is the nth term.

2.

What is the nth term of the sequence 2, 4, 6, 8, 10, ...?

2n

n + 2

2n - 2

n x (2 - 1)

The nth term of the sequence is 2n because each term is 2 times its position in the sequence.

3.

What is the 6^{th} term of the sequence 5, 10, 20, 40, 80, ...?

120

160

240

320

The sequence is doubling each time. So the 6^{th} term is 2 x 80 = 160.

4.

What is the next number in the sequence: 1^{1}, 2^{2}, 3^{3}, 4^{4}, ...?

3,125

625

125

256

The numbers in the sequence are n^{n}. So, the next number is 5^{5}, which is 3,125.

5.

What is the next number in the sequence: 6, 13, 20, 27, 34, ...?

41

39

43

42

The numbers in the sequence are rising by 7 each time.

6.

What sequence results from the rule 'subtract 3 from the previous term'?

1, -2, -5, -8, ...

1, 4, 7, 10, ...

3, 6, 9, 12, ...

-1, -3, -6, -9, ...

Starting with 1, if you subtract 3 from it, you get -2. If you subtract 3 from that, you get -5. So the sequence is 1, -2, -5, -8, ...

7.

What sequence is produced from the rule 'double the previous term and subtract 1'?

1, 1, 1, 1, ...

1, 3, 7, 15, ...

2, 4, 8, 16, ...

1, 2, 4, 8, ...

Starting with 1, if you double it and subtract 1, you get 2 - 1 = 1. If you double that and subtract 1, you get 2 - 1 = 1. So the sequence is 1, 1, 1, 1, ...

8.

Which term in the sequence 2, 6, 18, 54, ... is 1,458?

7th term

6th term

5th term

4th term

The sequence is multiplying each time by 3. So 1,458 comes after multiplying a further 3 times: 54 x 3 x 3 x 3 = 1,458, which makes it the 7th term.

9.

What is the 3^{rd} term of the geometric sequence where the first term is 4 and the common ratio is 3?

12

24

36

48

The nth term of a geometric sequence is a x r^{(n-1)}. So, a = 4, r = 3 and n = 3 gives 4 x 3^{2} = 4 x 9 = 36, which is the 3^{rd} term.

10.

What is the next number in the sequence: 2, 5, 10, 17, ...?

25

26

27

28

The numbers in the sequence are squares plus 1. So, the next number is 5^{2} plus 1, which is 26.