Final answer:
To find the 31st letter in the repeated sequence 'abcde', we divide 31 by 5 and find that it corresponds to the first letter in the cycle, which is 'a'.
Step-by-step explanation:
To find the 31st letter in the sequence abcdeabcdeabc..., we first need to determine the pattern of the sequence. Since it consists of a repeating pattern of 5 letters (a, b, c, d, e) in alphabetical order, we can divide the position we are looking for (31) by the length of the pattern (5).
The division gives us 31 ÷ 5 = 6 remainder 1. This means that after completing 6 full cycles of 5 letters each, we will be at the first letter of the next cycle. Therefore, the 31st letter is the same as the 1st letter of the pattern.
Thus, the 31st letter in the sequence is 'a'.