 # Practice - Sequences - 02

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 6th term of the sequence 5, 10, 20, 40, 80, ...?
120
160
240
320
The sequence is doubling each time. So the 6th term is 2 x 80 = 160.
4.
What is the next number in the sequence: 11, 22, 33, 44, ...?
3,125
625
125
256
The numbers in the sequence are nn. So, the next number is 55, 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 3rd 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 32 = 4 x 9 = 36, which is the 3rd 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 52 plus 1, which is 26.
Author:  Graeme Haw 