We have 3 patterns: I: A B C D ... X Y Z, which occurs only once. Y X ... B A, which repeats alternately. B C ... Y Z, which repeats alternately. Now, I: has 26 terms. So, number of terms before the desired term = (999 - 26) = 973.
Each of the patterns which occurs after I: has 25 letters.
Now, 973 ÷ 25 gives quotient = 38 and remainder = 23.
Thus, the 1000th trem of the given series is the 24th term of the 39th pattern after I:.
Clearly, the 39th pattern is II: and its 24th term is B.
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