An arithmetic sequence is a sequence of numbers in which each number is the sum of the two numbers before it. In this case, the sequence is 6, 12, 18, 24, 30, etc.
To find the number of multiples of 6 between 41 and 523, we can use the formula for the nth term of an arithmetic sequence:
a_n = a_1 + (n-1)d
where a_1 is the first term of the sequence, n is the number of terms, and d is the common difference between terms.
In this case, a_1 = 6 and d = 6. We can solve for n by plugging in the values for a_1 and d and solving for n:
523 = 6 + (n-1)6
517 = 6n - 6
523 = 6n
n = 87
Therefore, there are 87 multiples of 6 between 41 and 523.
Use an arithmetic sequence to find the number of multiples of 6 between 41 and 523. Justify your reasoning.
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