one of the letter from beginning and one of the letter from the end of a term are removed, one by one, alternate steps

The given series follows,

2

2 x 2 = 4

4 x 3 = 12

12 x 4 = 48

48 x 5 = 240.

Let first no. be "k" and multiple be "l"...start value of y with 3
then,
[(k x y) + {l x (l-1)}]
Thus, we get

15 x 3 + 3 x 2 = 51
51 x 4 + 4 x 3 = 216
216 x 5 + 5 x 4 = 1100
1100 x 6 + 6 x 5 = 6630
6630 x 7 + 7 x 6 = 46452

Therefore, the missing number is 6630.

The correct pattern is *1+1, *2+2, *3+3, *4+4, . . . . .
So,32 is wrong term and must be replaced by (10 * 3 + 3) = 33

$$\begin{gathered} 6 3 + 6 = 222 \\ \end{gathered}$$ 

Similarly ,  25 3 + 25 = 15650

In the given series,

 2nd term =  1 s t t e r m - 8 2 = 888 - 8 2 = 440  

 3rd term =  2 n d t e r m - 8 2 = 440 - 8 2 = 216  

and so on...

Here 6th term =  5 t h t e r m - 8 2 = 48 - 8 2 = 20

 Therefore, 22 is wrong.

In the given series, 

 2nd term = 1st term +  1 2= 4 +1 = 5  

3rd term = 2nd term +  2 2 =5+4= 9  

4th term = 3rd term +  3 2 =9+9=18  

5th term = 4th term +  4 2 = 18+16=34 

Therefore, odd term is 32

The series rtus/rtus/rtus/rtus. Thus, the pattern 'rtus' is repeated.

It follows the rule that

1

2x2  

3x3x3  

4x4x4x4  

5x5x5x5x5 

So the missing number is 4x4x4x4 = 256.

Here the first letter of the group is moved with a gap of one letter, the second letter of the group is backwardness and the third letter of the group is forwardness proceeding like this we get the letter group "JGW"