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

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

 

Here the letter series is alternative reverse order series. So we get P, N.

The difference of the two consecutive numbers are 1, 4, 9, 16, 25, 35. 

This is clearly , +12, +22, +32, +42, +52,+62 

Here 35 is wrong, So our wrong number is 91

First difference is 6 and second is 12. But if we take third as 18, then fourth difference will be 24. Then 93 can not be the last term.

So we have to take the difference as 6, 12, 24 and 48. 

So Answer is 21+24 = 45 

The first digit is formed by adding the numbers which are the results of powers of 2 increased by one and second letter is the corresponding alphabet to that number...last number is the next number to the first one...therefore

15=7+8 (i.e. 2^3)

O is corresponding alphabet to 15

and 16 comes after 15 

New sequence is as follows:

pr1  qr2  pr3  pq4  qr5  rp6  qq7  rp8  qp9  qr10  qp11  qp12

16th from the right  end is 7

$$\begin{gathered} b w x y z a \\ d s t u v c \\ f o p q r e \end{gathered}$$

Given series follows Cubes on Prime Numbers 

i.e 23, 33, 53,...but  93is 1331

so 1381 is wrong