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# Practice - Sequences - 06

Hello enthusiastic mathematicians! Ready to tackle sequences? This enticing KS3 Maths quiz will test your understanding of different sequence types, including arithmetic and geometric, and how to decipher them. Can you find the hidden patterns within the numbers and rise to the challenge? Access your inner mathematician, put your thinking cap on, and let's progress through this exciting mathematical journey together!
1.
Identify the pattern in the sequence -1, 2, 5, 8...
Each term is increased by a factor of 2
Each term increases by 3
Each term is doubled
Each term decreases by 1
This is an arithmetic sequence where each term increases by 3.
2.
What is the next number in the sequence: 1, 4, 9, 16, 25?
30
35
36
40
All the terms are squares of the natural numbers. So, the next square after 25 (5 x 5) is 36 (6 x 6).
3.
If the sequence starts -5, -3, -1, what is the common difference?
1
2
-2
-1
This is an arithmetic sequence, in which each number is increasing by 2.
4.
What is the 20th term in the sequence 3, 6, 9...?
54
57
60
63
This is an arithmetic sequence where each number increases by 3. The nth term is 3n, so the 20th term would be 3 x 20 = 60.
5.
Which number is missing in the sequence: 1, 4, 7, __, 13?
10
8
9
11
This is an arithmetic sequence, where each number increases by 3. Therefore, the missing number would be 7 + 3 = 10.
6.
What is the 5th term in the geometric sequence 2, 4, 8...?
16
32
64
128
This is a geometric sequence, where each term is multiplied by 2. The 5th term would be 25 or 2 x 2 x 2 x 2 x 2 = 32.
7.
What is the next number in the sequence: 2, 4, 6, 8?
10
9
11
12
This is an arithmetic sequence, where each number increases by 2. So, the next number would be 8 + 2 = 10.
8.
If the sequence starts 3, 6, 12, find the 5th term.
24
45
48
30
This is a geometric sequence where each term is multiplied by 2. The 5th term would be 3 x 2 x 2 x 2 x 2 = 48.
9.
What is the next term in the sequence 7, 10, 14, 19, 25?
32
30
31
33
This is an arithmetic sequence, but with an additional increasing sequence of 1 added each time. Therefore, the next term would be 25 + 6 + 1 = 32.
10.
What is the difference between 7th and 8th term in the sequence -5, -3, -1, etc?
1
2
3
4
In this arithmetic sequence, every term is 2 steps ahead of the previous one. Therefore, the difference between any two consecutive terms will always be 2.
Author:  Graeme Haw