Which letter-cluster will replace the question mark (?) to complete the given series?
EUGS, ?, HRJP, KOMM, OKQI

Let's observe the pattern of the letters across the clusters by skipping the unknown term first to identify the step size, or by testing the choices:
Let's check the progression between the known elements:

First letter: E → ? → H → K → O

From H to K is +3, K to O is +4.

This indicates a sequential increment: E(+1)→F(+2)→H(+3)→K(+4)→O.

So, the first letter is F.

Second letter: U → ? → R → O → K

From R to O is −3, O to K is −4.

This indicates a sequential decrement: U(−1)→T(−2)→R(−3)→O(−4)→K.

So, the second letter is T.

Third letter: G → ? → J → M → Q

From J to M is +3, M to Q is +4.

This follows a sequential increment: G(+1)→H(+2)→J(+3)→M(+4)→Q.

So, the third letter is H.

Fourth letter: S → ? → P → M → I

From P to M is −3, M to I is −4.

This follows a sequential decrement: S(−1)→R(−2)→P(−3)→M(−4)→I.

So, the fourth letter is R.

The missing cluster is FTHR.