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# Practice - Sequences - 04

Hello Whiz Kids! Welcome to a fun-filled maths quiz tailored just for you. The focus of this quiz is 'Sequences' - a crucial topic that forms the basis for many mathematical problems. It might seem tricky at first, but once you get the hang of it, sequences can be heaps of fun. So, put on your thinking caps and let’s dive right into this sequence extravaganza! Remember, there’s no rush - take your time and think your answers through. Good luck!
1.
In this sequence: 5, 10, 15, 20, ..., what is the term number of '35'?
6
7
8
9
The common difference in this sequence is 5. So, to find the term number you divide the term by the common difference. Therefore, 35 divided by 5 is 7.
2.
What comes next in this sequence: A, C, E, G, ...?
H
I
J
K
The letters in this sequence are skipping every second letter of the alphabet. After G, the next letter skipping one is I.
3.
What is the 6th term in the harmonic sequence: 1, 12, 13, 14,...?
15
16
17
18
The general formula for the nth term in a harmonic sequence is 1n. Therefore, the 6th term will be 16.
4.
What’s the 'common difference' in the following arithmetic sequence: 4, 7, 10, 13, 16, ...?
4
3
2
5
In an arithmetic sequence, the common difference is found by subtracting one term from the next. In this case, 7 - 4 or 10 - 7 gives a difference of 3.
5.
Which number completes the sequence: 1, 1, 2, 3, 5, 8, …?
11
13
12
10
This is a Fibonacci sequence where each number is the sum of the two preceding ones. So, 8 + 5 = 13.
6.
In the sequence 1, 32, 2... what is the 4th term?
52
62
34
14
The numbers are increasing by 12, so the next number is 2.5, or 52.
7.
How do you determine the 'common ratio' in a geometric sequence?
By subtracting successive terms
By dividing successive terms
By multiplying successive terms
In a geometric sequence, the common ratio is obtained by dividing any term by the preceding term.
8.
Which number comes next in the sequence: 3, 6, 9, 12, ...?
13
15
16
14
This is an arithmetic sequence, and each number increases by 3. Therefore, the next number in the sequence is 12 + 3 = 15.
9.
Identify the type of this sequence: 2, 4, 8, 16, ...
Arithmetic sequence
Geometric sequence
Fibonacci sequence
None of these
In a geometric sequence, each term after the first is found by multiplying the previous term by a fixed, non-zero number. In this case, the numbers are doubled each time.
10.
Which of the following sequences is not an arithmetic sequence?
2, 4, 6, 8,...
10, 20, 30, 40,...
5, 10, 15, 20,...
2, 4, 8, 16,...
An arithmetic sequence maintains a constant difference between every two consecutive terms. In the sequence '2, 4, 8, 16,...', the difference between terms is not constant, therefore it is not arithmetic. This is a geometric sequence.
Author:  Graeme Haw