Explanation:

Let’s break it down step by step:

- The given series: H, Q, I, T, K, ?, N

- Let’s look at positions in the alphabet:

H(8), Q(17), I(9), T(20), K(11), ?, N(14)

- Notice the pattern:

H to Q (+9), Q to I (-8), I to T (+11), T to K (-9), K to ? (let’s see), ? to N (need to fit +3 or -3 etc.)

- The jumps go +9, -8, +11, -9 — there’s a pattern: alternate positive/negative, and the magnitude increases by 1 each time.

- After -9, the next should be +13 (the increase is +2 each time: 9, 8, 11, 9... so now +13).

- K(11) + 13 = 24. That’s X.

Now, let’s see which option matches:

1. Y (not 24, but 25)

2. A (1)

3. U (21)

4. J (10)

So none of the provided options are X (24), so maybe let’s check if there’s an error with the sequence, or if a letter might fit better based on just observable alternate jumps and the available options.

- K (11) to N (14) is +3, so the missing letter (let’s call it M), would need to make the sequence logical.

- But honestly, with what’s given, none of the options fit the consistent jump logic, but if you want to keep that alternate sign jump, none work.

So, to answer directly:

- The correct answer should focus on the observable alternation.

- If you just align to the sequence and the options, none really fit perfectly, but based on what’s given and logical analysis, Y doesn’t fit the established pattern.

- The pattern is irregular in the options presented.

Here’s the thing: the next letter after K, considering pattern and options, none is a perfect fit, but the correct logical analysis points to "X," not "Y."

So, the answer isn’t option 1.