The word MATH is to be written multiple

Judelle Mejorada

Judelle Mejorada

Answered question

2022-09-20

The word MATH is to be written multiple times in this order: MATHMATHMATH...
If this continues infinitely, what is the 497th letter?

Answer & Explanation

madeleinejames20

madeleinejames20

Skilled2023-06-04Added 165 answers

To determine the 497th letter in the infinite repetition of the word MATH (MATHMATHMATH...), we need to observe the pattern in the repetition.
The word MATH has four letters: M, A, T, and H. When we repeat the word, the pattern continues in the same order: MATHMATHMATH...
Let's analyze the pattern by dividing the position (n) of a letter by 4 and examining the remainder. This will help us identify the corresponding letter at position n.
n0mod4: In this case, the letter is M.
n1mod4: In this case, the letter is A.
n2mod4: In this case, the letter is T.
n3mod4: In this case, the letter is H.
Now, let's determine the letter at position 497 using this pattern.
4971mod4
Since 497 leaves a remainder of 1 when divided by 4, the letter at position 497 is A.
Therefore, the 497th letter in the infinite repetition of the word MATH is A.

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