Alphabet Series Pattern Analysis

The question asks us to identify the next two terms in the given alphabetical series: A, C, F, J, ?, ?. We need to find the pattern governing the sequence of these letters.

Determining Letter Positions

First, let's find the position of each letter in the English alphabet:

• A is the $1^{st}$ letter.
• C is the $3^{rd}$ letter.
• F is the $6^{th}$ letter.
• J is the $10^{th}$ letter.

Identifying the Series Progression

Now, let's examine the difference between the positions of consecutive letters:

• Difference between C and A: $3 - 1 = 2$.
• Difference between F and C: $6 - 3 = 3$.
• Difference between J and F: $10 - 6 = 4$.

We observe a clear pattern here: the difference between consecutive terms is increasing by 1 each time (2, 3, 4). This suggests the next differences will be 5 and 6.

Calculating the Next Two Terms

Using the identified pattern, we can calculate the next two letters:

1. First missing term: Add the next difference (5) to the position of J (10). Calculation: $10 + 5 = 15$. The $15^{th}$ letter of the alphabet is O.
2. Second missing term: Add the subsequent difference (6) to the position of the new term (15). Calculation: $15 + 6 = 21$. The $21^{st}$ letter of the alphabet is U.

Therefore, the next two terms in the series are O and U.

Matching with Provided Options

The initial letter options provided contextually are:

• (A) O
• (B) U
• (C) R
• (D) V

Our calculated next two terms are O and U. This corresponds to option (A) for the first term and option (B) for the second term. The option stating "(A) and (B) respectively" accurately represents this sequence.