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Practice - Sequences - 01

Welcome to this fun-filled Maths quiz on Sequences! Here, you'll face 10 intriguing questions based on various types of sequences - arithmetic, geometric, and more. So put on your thinking caps, let your brain gears start turning and see if you can crack these number patterns. Who knows? You might find the rhythm in numbers more soothing than your favourite beat. Let's begin!
1.
Identify the next number in the sequence: 2, 6, 12, 20, ?
30
31
32
33
The pattern adds 4, then 6, then 8. Following that pattern, the next addition would be 10, making the next number 30.
2.
What will the 7th term be in this sequence: 3, 6, 12, 24...?
96
192
184
768
Each number in the sequence is twice the previous number. Hence, the 7th term would be 192.
3.
What is the 4th term of the sequence: 3, 6, 12... ?
24
48
96
192
The pattern here is to double the previous term. Thus the fourth term would be 2 x 3rd term = 2 x 12 = 24.
4.
How would you represent the nth term for the sequence: 5, 10, 15, 20...?
5n
n + 5
n - 5
5 ÷ n
Every term in this sequence is a multiple of 5. Hence the nth term can be represented as 5n.
5.
If a sequence follows the pattern 'multiply by 3, subtract 1', what is the third term starting from 2?
17
39
20
41
Starting from 2, you multiply by three (6) and subtract one (5) for the first term. Repeat that for the second term and you get 14. Repeat once more for the third term and get 41.
6.
What's the 5th term in the sequence: 2, 5, 11, 23... ?
45
47
48
50
Each term in the sequence is generated by doubling the previous term and adding one. So, the 5th term would be 2 x 23 + 1 = 47.
7.
What's the common difference in the arithmetic sequence: 10, 15, 20, 25... ?
2
5
7
10
The difference between each consecutive pair is 5, hence it's the common difference.
8.
What's next in the sequence: 1, 4, 9, 16, ?
20
21
24
25
The pattern here is that each term is the square of a natural number. So the next term would be 5 squared, which is 25.
9.
What common ratio connects the terms in the geometric sequence: 5, 15, 45, 135... ?
2
3
4
5
Each term is thrice the previous term, hence the common ratio is 3.
10.
Find the 10th term of the sequence: 7, 10, 13, 16... ?
34
35
36
37
The common difference here is 3 (each term + 3 = next term). The full sequence is 7, 10, 13, 16, 19, 22, 25, 28, 31, 34.
Author:  Graeme Haw