There are 43 numbers between 300 and 600 that are divisible by 7.
Step-by-step Explanation:
The reference indicates that we need to find numbers between 300 and 600 (exclusive of 300 and 600). Thus we're looking for numbers from 301 up to 599, that are divisible by 7.
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Find the first number divisible by 7: The first number greater than 300 that is divisible by 7 is 301 (since 301 = 7 * 43).
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Find the last number divisible by 7: The last number less than 600 that is divisible by 7 is 595 (since 595 = 7 * 85).
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Form an arithmetic sequence: The numbers divisible by 7 form an arithmetic sequence: 301, 308, 315, ..., 595. The common difference is 7.
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Use the arithmetic sequence formula: To find the number of terms in the sequence, we can use the formula:
n = (last term - first term)/ common difference + 1
where:
- n = number of terms
- first term = 301
- last term = 595
- common difference = 7
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Calculate the number of terms:
n = (595 - 301)/7 + 1
n = 294/7 + 1
n = 42 + 1
n = 43
Therefore, there are 43 numbers between 300 and 600 that are divisible by 7.
