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.

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

Each term in the series is obtained by adding 1 to the square of the preceding term.
So, missing term = (101)2 + 1 = 10202.

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

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

The given series is: 589654237, 89654237, 8965423, 965423, ?
Step 1: Observe the pattern in the series.
Step 2: The first number 589654237 loses the first digit '5' to become 89654237.
Step 3: The second number 89654237 loses the last digit '7' to become 8965423.
Step 4: The third number 8965423 loses the first digit '8' to become 965423.
Step 5: The fourth number 965423 loses the last digit '3' to become 96542.
Pattern Observed: The series alternates between removing the first digit and the last digit.
Final Step: Following this pattern, the next number after 965423 should be 96542 (removing the last digit '3').
Thus, the correct answer is: 96542 (Option D).

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

Clearly, 2 x 3 = 6, 6 x 3 = 18, 18 x 3 = 54,.....
So, the series is a G.P. in which a = 2, r = 3.
Therefore 8th term = ar8-1 = ar7 = 2 x 37 = (2 x 2187) = 4374.

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

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

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

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

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

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

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

The pattern is - 21, - 19, - 17, - 15,.....
So, missing term = 48 - 13 = 35.