The given sequence is a combination of three series :

I. 1st, 4th, 7th, 10th, 13th terms i.e. 2, 4, 6, 8, ?
II. 2nd, 5th, 8th, 11th terms i.e. 1, 4, 7, 10
III. 3rd, 6th, 9th, 12th terms i.e. 2, 5, 8, 11

Clearly, I consists of consecutive even numbers. So, the missing term is 10.

The series consists of squares and cubes of consecutive natural numbers i.e. 12, 13, 22, 23, 32, 33, 42, .....
So, missing term = 43 = 64.

The pattern is - 4, - 9, - 16,.....i.e. - 22, - 32, - 42,.....
So, missing pattern = 169 - 52 = 169 - 25 = 144.

The pattern is + 1, x 1, + 2, x 2, + 3, x 3, + 4, x 4, + 5.
So, missing term = 13 x 3 = 39.

The pattern is x 3, + 4, x 5, + 6, x 7,.....
So, missing term = 1127 + 8 = 1135.

The terms of the given series are (22 - 1), (42 - 1),....., (82 - 1), (102 - 1), (122 - 1).
So, missing term = (62 - 1) - (36 - 1) = 35.

Let's break down this number series question!

The series is: 1, 2, 3, 6, 9, 18, ?, 54

Look for a pattern. It's not a simple addition or subtraction.

Notice this:
1 + 2 = 3
3 + 6 = 9
9 + 18 = ?

It looks like each number is the sum of the two numbers before it.

So, to find the missing number: 9 + 18 = 27

Therefore, the missing number is 27. The correct answer is B.

Double-check: 18 + 27 = 45 (Incorrect so that Logic is wrong)

Notice this new Logic:
1 x 2 = 2
2 x (3/2) = 3
3 x 2 = 6
6 x (3/2) = 9
9 x 2 = 18
18 x (3/2) = ?
So, to find the missing number: 18 x (3/2) = 27
Then check it with the next number: 27 x 2 = 54

Therefore, the missing number is 27. The correct answer is B.

Clearly, the given series consists of prime numbers starting from 2. So, the missing
term is the prime number after 11, which is 13.

The pattern is + 3, + 4, + 5, + 6,.....
So, missing term = 9 + 5 = 14.

The given sequence is a combination of two series :
I. 3, 7, 13, 21, 31, ? and II. 4, 7, 13, 22, 34
The pattern in I is + 4, + 6, + 8, + 10,.....
The pattern in II is + 3, + 6, + 9, + 12,.....
So, missing term = 31 + 12 = 43.

The pattern is - 45, - 35, - 25, .....
So, missing term = 20 - 15 = 5.

The given series consists of cubes of natural numbers only. 256 is not the cube of
any natural number.

Clearly, 5 x 2 = 10, 10 x 2 = 20, 20 x 2 = 40,.....
So, the series is a G.P. in which a = 5 and r = 2.
Let 1280 be the rath term of the series.
Then, 5x2n-1 = 1280 ⇔ 2n-1 = 256 = 28 ⇔ n - 1 = 8 ⇔ n = 9.

The pattern is + 2, + 4, + 8, + 16,.....
So, missing term = 28 + 8 = 36.

The sum of any three consecutive terms of the series gives the next term.
So, missing number = 8 + 15 + 27 = 50.

The pattern is + 1, + 3, + 6,....., i.e. + 1, + (1, + 2), + (1 + 2 + 3),.....
So, missing term = 15 + (1 + 2 + 3 + 4) = 25.

The pattern is + 6, + 9, + 12, + 15, .....
So, missing term = 21 + 12 = 33.

The pattern is x 2 + 1, x 2 - 1, x 2 + 1, x 2 - 1,.....
So, missing term = 101 x 2 + 1 = 203.

Clearly, 90 = 30 x 3, 180 = 6 x 30, 12 = 2 x 6, 50 = 25 x 2, 100 = 4 x 25, 200 = 50 x 4.
So, missing term = 3 x 50 = 150.

The given sequence is a combination of two series:
I. 13, 24, 35, 46, 57 and II. 32, 43, ?, 65, 76
The pattern in both I and II is + 11. So, missing term = 43 + 11 = 54.