A pattern is formed using the letters A, B and C. The first 15 letters are show. A B A C A A B A C A A B A C A ...... 1st 15th The letter A appears 137 times in the pattern. What is the greatest possible number of letters in the pattern? Read LessInteractive Thinking Tool 1Solution & Explanation:View AllShow the pattern you have found. Explain your steps.
Question
A pattern is formed using the letters A, B and C. The first 15 letters are show. A B A C A A B A C A A B A C A ...... 1st 15th The letter A appears 137 times in the pattern. What is the greatest possible number of letters in the pattern? Read LessInteractive Thinking Tool 1Solution & Explanation:View AllShow the pattern you have found. Explain your steps.
Solution
The pattern in the sequence is ABACAA. This pattern repeats every 6 letters.
In the pattern, the letter 'A' appears 4 times. So, if 'A' appears 137 times in the pattern, the pattern has repeated 137/4 = 34.25 times.
Since the pattern cannot repeat a fractional number of times, it must have repeated 34 times fully and then started the 35th repetition.
In the 35th repetition, only the first letter 'A' is needed to make the total count of 'A' as 137.
So, the total number of letters in the pattern is 34 (full repetitions) * 6 (letters in each repetition) + 1 (the first letter of the 35th repetition) = 205.
Therefore, the greatest possible number of letters in the pattern is 205.
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