In the following question, select the missing number from the given series.

9, 11, 14, 16, 19, 21, ?

 

The given series follows,

2

2 x 2 = 4

4 x 3 = 12

12 x 4 = 48

48 x 5 = 240.

The given series follows a pattern that,

19 x 19 x 19 = 6859

18 x 18 x 18 = 5832

17 x 17 x 17 = 4913

16 x 16 x 16 = 4096

15 x 15 x 15 = 3375

So, the missing number in the given series = 4913  

The given series follows a logic that

11 x 12, 12 x 13, 13 x 14, 14 x 15, 15 x 16,...

So the missing number is 13 x 14 = 182

The given series follows the pattern that

So the missing number is  37 + 38 = 75

75 + 66 = 141

....

The pattern of given series is :

5

14 = (5x3) - 1

45 = (14x3) + 3

130 = (45x3) - 5

(?) = (130x3) + 7

=> (?) = 397

1182 = (397x3) - 9

Thus, the missing number is 397.

It follows the rule that

1

2x2  

3x3x3  

4x4x4x4  

5x5x5x5x5 

So the missing number is 4x4x4x4 = 256.

26 - 6 = 20

20 - 5 = 15

15 - 4 = 11

11 - 3 = 8

8 - 2 = 6

6 - 1 = 5

Therefore, 16 is wrong number.

Two series alternate here, with every third number following a different pattern.
In the main series, 4 is added to each number to arrive the next.
In alternate series, 5 is subtracted from each number t arrive the next number.
Here in the main series
3 + 4 = 7
7 + 4 = 11
11 + 4 = 15
15 + 4 = 19

In alternate series
24 - 5 = 19
19 - 5 = 14...