Series Pattern Analysis

To find the missing letter cluster in the series DKM, FJP, HIS, JHV, ?, we need to analyze the pattern between consecutive terms.

Let's examine the positional changes of the letters in the alphabet:

• Term 1 to Term 2 (DKM to FJP):
  • D (4) to F (6): $+2$
  • K (11) to J (10): $-1$
  • M (13) to P (16): $+3$
• Term 2 to Term 3 (FJP to HIS):
  • F (6) to H (8): $+2$
  • J (10) to I (9): $-1$
  • P (16) to S (19): $+3$
• Term 3 to Term 4 (HIS to JHV):
  • H (8) to J (10): $+2$
  • I (9) to H (8): $-1$
  • S (19) to V (22): $+3$

The consistent pattern observed is adding 2 to the first letter's position, subtracting 1 from the second letter's position, and adding 3 to the third letter's position.

Applying the Pattern to Find the Next Term

We apply the established pattern (+2, -1, +3) to the last term (JHV):

• First letter: J (10) + 2 = 12, which corresponds to the letter L.
• Second letter: H (8) - 1 = 7, which corresponds to the letter G.
• Third letter: V (22) + 3 = 25, which corresponds to the letter Y.

Therefore, the next letter cluster in the series is LGY.