Hey there Maths whizz! Think you got what it takes to crack the mystery of sequences? If numerical patterns tickle your curiosity, then it's your time to shine. Jump right in and test your knowledge of arithmetic and geometric sequences, common differences, patterns and all that exciting stuff. Don't worry, it's as fun as it sounds! Good luck!

1.

What is the sequence generated by the rule 'start at 2, then multiply each term by 3'?

2, 3, 6, 9, 12

2, 6, 18, 54, 162

2, 5, 8, 11, 14

2, 4, 9, 27, 81

Each term is three times the preceding term, beginning with 2.

2.

Identify the 7th term in the Fibonacci sequence (starting with 1, 1)

8

11

13

21

In a Fibonacci sequence, each term (after the first 2) is the sum of the two preceding terms. So, the first 7 terms are = 1, 1, 2, 3, 5, 8, 13.

3.

Find the next number in the sequence: 5, 15, 45, 135, …

315

405

515

605

This sequence multiplies each term by 3 to get the next. Hence, 135 x 3 = 405.

4.

Identify the 10th term of the sequence: 5, 10, 15, 20,...

40

45

50

55

This is an arithmetic sequence with a common difference of 5. So, 10th term is 5 x 10 = 50.

5.

In the arithmetic sequence 2, 4, 6, ..., what is the common difference?

1

2

3

4

The difference between consecutive numbers in the sequence is 2.

6.

If the common difference of an arithmetic sequence is 6 and the first term is 2, what's the fifth term?

22

26

28

30

The nth term is 6n - 4, so the 5th term is 26.

7.

What is the common ratio of the geometric sequence 3, 9, 27, 81...

2

3

4

5

The common ratio is found by dividing any term by the preceding term, so 9 ÷ 3 = 3.

8.

What is the first term of the sequence if the third term is 18 and common difference is 6?

6

8

10

12

If we go backwards two spots from the third term with a common difference of 6, the first term will be 18 - 2 x 6 = 6.

9.

What type of sequence is this: 10, 20, 40, 80, 160...

Arithmetic Sequence

Geometric Sequence

Fibonacci Sequence

None of the Above

This is a Geometric sequence because each term after the first is found by multiplying the previous term by 2.

10.

What is the sum of the first five terms in the arithmetic sequence 2, 4, 6, 8, 10...

15

20

25

30

Just add the first 5 terms together. 2 + 4 + 6 + 8 + 10 = 30.