What Comes Next? Trivia Quiz

Answer: 21

In this sequence you'll notice that the difference between each pair of numbers gets incremented by 1 as you move ahead in the sequence:

1 = 0 + 1
3 = 1 + 2
6 = 3 + 3
10 = 6 + 4
15 = 10 + 5

And so the missing number in the sequence must be greater than the previous number by 6.

Therefore,
x = 15 + 6 = 21

And so the missing number is 21.

Answer: 3125

This one's slightly tricky:

In this sequence, consecutive positive integers are each raised to the power of themselves. In mathematical language, if 'n' is a positive integer, then:

n^n = a

where 'a' is a number in the sequence. Here,

1^1 = 1
2^2 = 4
3^3 = 27
4^4 = 256

And so the next number in the sequence (x) is equal to 5^5, which is 3125.

Answer: 34

This really is my favourite sequence. :-)

Here, each number is equal to the sum of the two numbers preceding it:

2 = 1 + 1
3 = 2 + 1
5 = 3 + 2
8 = 5 + 3
13 = 8 + 5
21 = 13 + 8

The value of 'x' will hence be the sum of 21 and 13, which is 34.

This is special sequence of numbers known as the "Fibonacci Sequence". This sequence was first described by Leonardo of Pisa, a.k.a. Fibonacci, in 1200 AD, to describe the growth of rabbit-population!

This sequence also has a number of practical applications today, which you can read about at this page: http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/fibnat.html#spiral
I highly recommend giving it a read, it is very interesting.

Answer: 256

Pretty straightforward: each number is exactly twice the previous number. And so 'x' should be twice of the number preceding it, which is 128:

x = 2 * 128 = 256

And hence 256 is the answer.

Another way to look at it is that each number is a consecutive power of 2:

1 = 2^0
2 = 2^1
4 = 2^2
8 = 2^3
16 = 2^4
32 = 2^5
64 = 2^6
128 = 2^7

And 256 = 2^8.

Answer: 21

Here, 3 and 2 are alternately added to the previous number in the sequence:

1 + 3 = 4
4 + 2 = 6
6 + 3 = 9
9 + 2 = 11
11 + 3 = 14
14 + 2 = 16
16 + 3 = 19

And so the next number will be equal to 19 + 2, which is 21.

Answer: 0

In this sequence you alternately subtract 2 and add 1:

3 - 2 = 1
1 + 1 = 2
2 - 2 = 0
0 + 1 = 1
1 - 2 = -1

Adding 1 to -1, we get 0, which is the answer.

Answer: 9

Easy enough- consecutive odd numbers: the next odd number after 7 is 9, which is the answer.

Answer: 343

This is the series of cubes of consecutive natural numbers:

1^3 = 1
2^3 = 8
3^3 = 27
4^3 = 64
5^3 = 125
6^3 = 216

And the next number is the cube of 7 (7^3), which is 343.

Answer: 99

The rule here is to take 1 less than the squares of consecutive whole numbers. So if 'n' is a whole number, we take (n^2 - 1):

-1 = 0 - 1 = 0^2 - 1
0 = 1 - 1 = 1^2 - 1
3 = 4 - 1 = 2^2 - 1
8 = 9 - 1 = 3^2 - 1
15 = 16 - 1 = 4^2 - 1
24 = 25 - 1 = 5^2 - 1
35 = 36 - 1 = 6^2 - 1
48 = 49 - 1 = 7^2 - 1
63 = 64 - 1 = 8^2 - 1
80 = 81 - 1 = 9^2 - 1

And so the next number in the series should be 1 less than the square of 10.

x = 10^2 - 1
=> x = 100 - 1
=> x = 99

Hence, the value of x is 99.

This is what I had in mind while writing this question, but if you look closely, there's a much more obvious pattern that this sequence follows. I won't spoil it for you and leave it for you to find; that is, unless you have already! I have to admit I hadn't noticed it myself until a few people wrote to me about it... it's truly fascinating how the two "rules" produce the same sequence.

Answer: 1

In this sequence you alternately subtract 2 and add 3:

-1 = 1 - 2
2 = -1 + 3
0 = 2 - 2
3 = 0 + 3

And so the value of 'x' must be 2 less than that of the number directly preceding it:
x = 3 - 2 = 1
Therefore, the answer is 1.

Answer: 42

In this pattern you just have consecutive multiples of 7:

7 = 7 1
14 = 7 * 2
21 = 7 * 3
28 = 7 * 4
35 = 7 * 5

The value of 'x' is (7 * 6), which is 42.

Answer: 29

In this sequence, the difference between two consecutive numbers goes on getting incremented by 1:

2 = 1 + 1
4 = 2 + 2
7 = 4 + 3
11 = 7 + 4
16 = 11 + 5
22 = 16 + 6

'x' will be equal to the sum of the preceding number and 7,

x = 22 + 7 = 29

Hence, the value of 'x' is 29.

Answer: 17

Alternately add 7 and subtract 3:

1 + 7 = 8
8 - 3 = 5
5 + 7 = 12
12 - 3 = 9
9 + 7 = 16
16 - 3 = 13
13 + 7 = 20

The value of 'x' will be 3 less than 20, and so 'x' is equal to 17.

Answer: 122

Note that here the differences between consecutive numbers in the series are 1, 3, 9 and 27: consecutive powers of 3.

2 = 1 + 1 = 1 + 3^0
5 = 2 + 3 = 2 + 3^1
14 = 5 + 9 = 5 + 3^2
41 = 14 + 27 = 14 + 3^3

Now, 3^4 = 81, and so we can get the value of 'x' by adding 81 to the number preceding it:

x = 41 + 3^4
=> x = 41 + 81
=> x = 122

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Another way of going about solving this one is to treble each number and then subtract one, in each case, the answer is the same! (Thanks to all the people who wrote in to mention this!)

Answer: 8

I hope you enjoyed playing this quiz!