Letter Cluster Series Analysis

The question asks to find the next term in the letter cluster series: FZ, GA, JZ, OA, ? To solve this, we need to identify the pattern governing the changes in the letters.

First Letter Pattern

Consider the first letter of each cluster: F, G, J, O.

• Find the position of each letter in the alphabet: F is 6th, G is 7th, J is 10th, O is 15th.
• Calculate the difference between the positions of consecutive letters:
  • G (7) - F (6) = $7 - 6 = 1$
  • J (10) - G (7) = $10 - 7 = 3$
  • O (15) - J (10) = $15 - 10 = 5$
• The differences are 1, 3, 5. This sequence increases by 2 each time ($1, 1+2=3, 3+2=5$).
• The next difference in the sequence should be $5 + 2 = 7$.
• Add this difference to the position of the last letter (O): $15 + 7 = 22$.
• The 22nd letter of the alphabet is V.

Second Letter Pattern

Now, examine the second letter of each cluster: Z, A, Z, A.

• This sequence alternates between the letters Z and A.
• Following the pattern Z, A, Z, A, the next letter must be Z.

Completing the Series

Combining the determined next first letter (V) and the next second letter (Z), the missing cluster is VZ.

Therefore, VZ replaces the question mark.