There are 74 numbers between 50 and 570 that are divisible by 7.
To determine this, we can follow these steps:
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Find the first multiple of 7 greater than 50: Dividing 50 by 7 gives approximately 7.14. The next whole number, 8, multiplied by 7 is 56. So, 56 is the first number divisible by 7 in our range.
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Find the last multiple of 7 less than 570: Dividing 570 by 7 gives approximately 81.43. The greatest whole number less than this, 81, multiplied by 7 is 567. So, 567 is the last number divisible by 7 in our range.
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Determine the number of multiples: The multiples of 7 form an arithmetic sequence: 56, 63, 70,... 567.
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The nth term of this sequence can be expressed as an = 56 + (n-1)7.
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To find the number of terms, we set an = 567 and solve for n:
567 = 56 + (n-1) 7
511 = (n-1) 7
73 = n - 1
n = 74
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Therefore, there are 74 numbers between 50 and 570 that are divisible by 7.
We can compare this to the provided reference, which states that there are 64 integers between 50 and 500 divisible by 7. This confirms our methodology is correct, and since our question extends to 570, it’s reasonable to find a larger total.
