Questions: Alex wrote out the entire alphabet (a-z), in order, 5 times in a row. (Alex wrote the entire alphabet for the first time, then for the second, third, fourth, and fifth time.) What was the 100th letter Alex wrote? A) w B) v C) u D) t

Alex wrote out the entire alphabet (a-z), in order, 5 times in a row. (Alex wrote the entire alphabet for the first time, then for the second, third, fourth, and fifth time.) What was the 100th letter Alex wrote?
A) w
B) v
C) u
D) t

Transcript text: 43. Alex wrote out entire alphabet (a-z), in order, 5 times in a row. (Alex wrote entire alphabet for the first time, then for the second, third, fourth, and fifth time.) What was the 100 th letter Alex wrote? A) w B) v C) $u$ D) t

Solution

Solution Steps

Step 1: Determine the total number of letters in one full alphabet

The English alphabet has 26 letters (from $ a $ to $ z $).

Step 2: Calculate the total number of letters written by Alex

Alex wrote the alphabet 5 times in a row. Therefore, the total number of letters written is: \[ 5 \times 26 = 130 \]

Step 3: Find the position of the 100th letter within the sequence

Since the sequence repeats every 26 letters, we can find the position of the 100th letter by calculating the remainder when 100 is divided by 26: \[ 100 \div 26 = 3 \text{ with a remainder of } 22 \] This means the 100th letter corresponds to the 22nd letter in the alphabet.

Step 4: Identify the 22nd letter in the alphabet

The 22nd letter in the English alphabet is $ v $.

Thus, the 100th letter Alex wrote is $ v $.