Series Completion Logic

The question asks us to find the correct sequence of letters to fill in the blanks within a given letter series, making it a complete and logical pattern. The goal is to identify the repeating sequence that governs the series.

The series provided is:

T _ D S _ R _ S T R D _ T _ D S _ R _ S

Series Structure Analysis

We need to analyze the structure of the series to uncover the underlying pattern. Let's count the characters:

• Total characters in the series: 20.
• Number of visible letters: 13.
• Number of blanks (_): 7.

The series structure looks like this, indicating the positions of the fixed letters and the blanks:

T [blank1] D S [blank2] R [blank3] S T R D [blank4] T [blank5] D S [blank6] R [blank7] S

By observing the arrangement of the letters, particularly sequences like S T R D and the initial T, we can hypothesize a repeating pattern. Let's test the pattern TRDS, as it seems plausible given the letters present.

If the pattern is TRDS, and the total series length is 20, the pattern would repeat 5 times (since 20 / 4 = 5). The expected sequence is:

T R D S T R D S T R D S T R D S T R D S

Now, let's verify this hypothesis by comparing the pattern with the fixed letters provided in the original series.

The table confirms that the hypothesized TRDS pattern aligns perfectly with all the fixed letters given in the original series. This confirms the pattern is correct.

Pattern Application Steps

With the repeating pattern TRDS confirmed, we can now determine the specific letters needed to fill each of the 7 blanks. The pattern sequence is:

T₁ R₂ D₃ S₄ T₅ R₆ D₇ S₈ T₉ R₁₀ D₁₁ S₁₂ T₁₃ R₁₄ D₁₅ S₁₆ T₁₇ R₁₈ D₁₉ S₂₀

We identify the letters corresponding to the blank positions (2, 5, 7, 12, 14, 17, 19):

• Blank at Position 2: The 2nd letter in the TRDS pattern is R.
• Blank at Position 5: The 5th letter (1st of the second repetition) is T.
• Blank at Position 7: The 7th letter (3rd of the second repetition) is D.
• Blank at Position 12: The 12th letter (4th of the third repetition) is S.
• Blank at Position 14: The 14th letter (2nd of the fourth repetition) is R.
• Blank at Position 17: The 17th letter (1st of the fifth repetition) is T.
• Blank at Position 19: The 19th letter (3rd of the fifth repetition) is D.

Blank Filling Sequence

Collecting the letters found for each blank in order, we get the sequence required to complete the series.

The combination of letters is: R, T, D, S, R, T, D.

This sequence correctly fills the blanks in the original series to form the repeating pattern TRDS.