Identifying the Pattern in the Alphabet Sequence

The given sequence is B, D, F, H... We need to find the 6^th letter in this sequence.

First, let's identify the pattern by looking at the positions of these letters in the English alphabet:

• B is the 2^nd letter.
• D is the 4^th letter.
• F is the 6^th letter.
• H is the 8^th letter.

The sequence of positions is 2, 4, 6, 8... This is an arithmetic progression where the first term ($a_1$) is 2 and the common difference ($d$) is 2 (since each subsequent letter's position increases by 2).

Calculating the 6^th Term

We can use the formula for the $n^{th}$ term of an arithmetic progression:

$ a_n = a_1 + (n-1)d $

Here, we want to find the 6^th term ($n=6$), the first term $a_1 = 2$, and the common difference $d = 2$.

Substitute the values into the formula:

$ a_6 = 2 + (6-1) \times 2 $

$ a_6 = 2 + (5) \times 2 $

$ a_6 = 2 + 10 $

$ a_6 = 12 $

Determining the 6^th Letter

The calculated position for the 6^th letter in the sequence is 12.

The 12^th letter of the English alphabet is L.

Therefore, the 6^th letter in the sequence B, D, F, H... is L.