Select the option that represents the letters that, when sequentially placed from left to right in the blanks below, will complete the letter series.
P __ MO_ST_OP _ TM __ S_MO

The given fragment is

$$P\; \_ \_ \; M O \_ S T \_ O P \_ T M \_ \_ S \_ M O$$

We must discover a fixed pattern and then insert the 8 missing letters (one for each blank) so that the series is completed.

Step 1 : Look for a short repeating block
Write out the known letters in the order they appear and look for repetition:

$$P\;\; M O\;\; S T\;\; O P\;\; T M\;\; S\; M O$$

They can be rearranged into the 5-letter block
$$P\,S\,T\,M\,O$$
Indeed, if we write $$PSTMO$$ again and again, we obtain

$$P \, S \, T \, M \, O \; P \, S \, T \, M \, O \; P \, S \, T \, M \, O \; P \, S \, T \, M \, O$$

Step 2 : Match the block to the given fragment

Index the letters of the repeated pattern:

1 P, 2 S, 3 T, 4 M, 5 O, 6 P, 7 S, 8 T, 9 M, 10 O, 11 P, 12 S, …

Comparing this list with the fragment:

1 P (given) 2 S (blank 1) 3 T (blank 2) 4 M (given) 5 O (given) 6 P (blank 3) 7 S (given) 8 T (given) 9 M (blank 4) 10 O (given) 11 P (given) 12 S (blank 5) 13 T (given) 14 M (given) 15 O (blank 6) 16 P (blank 7) 17 S (given) 18 T (blank 8) 19 M (given) 20 O (given)

Thus the required sequence of missing letters is

blank 1 → S, blank 2 → T, blank 3 → P, blank 4 → M, blank 5 → S, blank 6 → O, blank 7 → P, blank 8 → T

Step 3 : Assemble the answer

The eight letters, left to right, are
$$S\;T\;P\;M\;S\;O\;P\;T$$

Option A provides exactly this order: STPMSOPT.

Hence, the correct completion and the correct option is:

Option A which is: STPMSOPT