What should come next in the following letter sequence?

A A B A B C A B C D A B C D E A B C D

Second vowel from the right of reversed English alphabet is E and 7th letter to the left of E in the new series is L.

2nd letter to the left of 17th letter from the right means (2 + 17 = ) 19th letter from the right = (26 - 19 + 1 =) 8th letter from the left end , i.e H.  Thus, 8th letter falls into the second section of the reversed sequence. Now, the sequence FGHIJ is reversed and becomes JIHGF. Clearly, position of H remains unchanged. Hence the required letter is H.

4th to the right of 20th letter from the right means (20 - 4 =) 16th from the right.

16th letter from the right = (26 - 16 + 1 =) 11th from the left, i.e K

If the first half of the English alphabet is reversed and the remaining part has been left undisturbed, then it becomes very easy to find out the required letters, if required letters come in the first half. According to the question, 10th to the left of 16th letter from the left = (16 - 10 =) 6th letter from the left in new series.

=>  6th letter from the left in new series = (13 + 1 - 6=) 8th letter from the left in the original series, i.e H.

Find out the positions of both the letters from the left and divide the sum of the positions of both the letters from the left by 2. Here 13+23=36. Now divide 36 by 2 , i.e 18. Hence R is the required letter.

First letters are common. Second letters are:b, c, c, c, c. One of the four words having c is the last word. Let us see the third letters now ,there are: t, c, q, h. Clearly t is the last. Hence Actuate is the last word. 

The given word is VITREOUS. Of which , TRSV are the consonants and IEOU are the vowels. Now, after making the changes as given in the question  we get following arrangment: RSTVEIOU.

Again from precalculation, we know that second to the right of fourth  from the left means (2+4=) 6th from the left. i.e I

Given word is O B S E R V A N T. After making the change as given in the question, we get the following arrangement:

T N A V R E S B O.