What letters will fill the blank?

Z, X, V, T, R, __,__

The series is a b c c a b | b c a a b c | a b c c a b

Here, the pattern a b c c a b | b c a a b c is repeated alternatively.

Here 'bccb' repeated 3 times.

b c c b | b c c b | b c c b 

Here it can be seen that it is not a continuous series.

so take alternative terms.

CGE, FJH, IMK and RNP, OKM,__

Between R and O there is a gap of two letters. so the first letter in the answer is L.Proceding like this the answer is LHJ

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"

The difference between consecutive numbers of the given series are respectively 5, 7, 9, 11, 13, and 15.

Therefore, 24+11=35 But in your problem it is given as 34.so 34 is wrong number

Here the number follows the given rule 

 $$\begin{gathered} 23-1, 33-1, 43-1, 53-1, ... \\ \end{gathered}$$

But 28 has been given in problem series.

so 28 is wrong number.

Here the series of the form is x2 - 1, x2 - 2, x2 - 3,...

 53 x 2 - 4 = 106 - 4 = 102

$$\begin{gathered} 2 = 12 + 1 \\ 3 = 22 - 1 \\ 10 = 32 + 1 \\ Now 102 - 1 = 99 \\ 9802 = 992 + 1 \end{gathered}$$