There are 43 numbers divisible by 7 between 200 and 500.
To determine this, we need to find the first and last multiples of 7 within the given range.
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First Multiple of 7 Greater Than 200: Divide 200 by 7, which gives approximately 28.57. Therefore, the first multiple of 7 greater than 200 is 29 * 7 = 203.
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Last Multiple of 7 Less Than 500: Divide 500 by 7, which gives approximately 71.43. Therefore, the last multiple of 7 less than 500 is 71 * 7 = 497.
Now we know the sequence of multiples of 7 between 200 and 500 is: 203, 210, 217,... 497. This is an arithmetic sequence with a common difference of 7.
To find the number of terms in this sequence, we can use the formula:
Number of terms = (Last term - First term) / Common difference + 1
Number of terms = (497 - 203) / 7 + 1
Number of terms = 294 / 7 + 1
Number of terms = 42 + 1
Number of terms = 43
Therefore, there are 43 numbers divisible by 7 between 200 and 500.
