Hello future mathematicians! Time to put your skills to the test. Ready for a delightful challenge that will help illuminate the wonderful world of sequences? Mischievous integers and rebellious fractions are all part of this fun journey. So, here's your opportunity to prove your mettle. Remember, mistakes are just steps on the journey towards a solution! Buckle up, and let's delve into the exciting realm of sequences.

1.

What is the next term in the sequence: 1, 4, 9, 16...

20

23

25

27

2.

Identify the missing number in this sequence: 6, 18, ?, 78, 126, 186

24

36

42

48

Each term in this series adds 12 more than the previous addition. So, 18 + 24(next addition) = 42.

3.

What is the next number in the sequence: 2, 4, 8, 16...?

20

24

32

64

Each number in this series is doubled to get the next. Thus, 16 x 2 = 32.

4.

Which number should replace the question mark in the sequence: 12, 24, 36, ?, 60

42

45

48

50

This is a sequence of multiples of 12. Hence, the missing term is 12 x 4 = 48.

5.

Find the common difference in the arithmetic sequence: 5, 8, 11, 14, 17...

2

3

4

5

The common difference in an arithmetic sequence is the difference between any two consecutive terms. Here, each term increases by 3.

6.

Find the 10^{th} number in the sequence: 1, 3, 6, 10, 15...

45

50

55

60

This is a sequence of triangular numbers. The 10^{th} term would be 10 x (10+1) ÷ 2 = 55.

7.

Identify the 7^{th} term in the sequence: 3, 6, 9, 12....

15

18

21

24

The sequence increases by 3 each time. The 7^{th} term is 3 multiplied by 7, which is 21.

8.

Find the missing term in the Fibonacci sequence: 1, 1, 2, 3, 5, ?, 13...

7

8

9

10

Each number in a Fibonacci sequence is the sum of the two preceding ones. Hence, 5 + 3 gives the missing term 8.

9.

What is the next term in the sequence: 1^{1}, 2^{2}, 3^{3}, 4^{4}...?

54

125

243

3,125

Each term of the sequence is a number raised to its own power. Hence, the next term is 5^{5} = 3,125.

10.

What is the common ratio in the geometric sequence: 4, 12, 36, 108...?

2

3

4

12

The common ratio in a geometric sequence is the ratio of any two consecutive terms. Here, the number is multiplied by 3 each time.

^{2}= 25.