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.

What is the 6th term in the harmonic sequence: 1, ^{1}⁄_{2}, ^{1}⁄_{3}, ^{1}⁄_{4},...?

2.

How do you determine the 'common ratio' in a geometric sequence?

By subtracting successive terms

By dividing successive terms

By adding successive terms

By multiplying successive terms

In a geometric sequence, the common ratio is obtained by dividing any term by the preceding term.

3.

In the sequence 1, ^{3}⁄_{2}, 2... what is the 4th term?

The numbers are increasing by ^{1}⁄_{2}, so the next number is 2.5, or ^{5}⁄_{2}.

4.

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.

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.

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.

7.

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.

8.

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.

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.

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.

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^{1}⁄_{n}. Therefore, the 6th term will be^{1}⁄_{6}.