There are 64 integers between 50 and 500 that are divisible by 7.
Understanding the Solution
To find the number of integers divisible by 7 between 50 and 500, we can use an arithmetic progression (A.P.) approach.
- First Term: The first integer greater than 50 divisible by 7 is 56.
- Last Term: The largest integer less than 500 divisible by 7 is 497 (500 divided by 7 leaves a remainder of 3).
- Common Difference: The common difference between consecutive terms is 7.
Using the formula for the nth term of an A.P., an = a1 + (n-1)d, where an is the nth term, a1 is the first term, n is the number of terms, and d is the common difference, we can solve for n:
497 = 56 + (n-1)7
Solving for n, we get n = 64. Therefore, there are 64 integers between 50 and 500 divisible by 7. Multiple sources confirm this result, as shown in the provided references.
References and Supporting Evidence
The provided references consistently support the answer of 64. They detail the steps involved in calculating the number of integers using the arithmetic progression method, identifying the first and last terms divisible by 7 within the specified range.
For example, this reference explicitly states, "Hence, there are 64 numbers between 50 and 500 which are divisible by 7." Other sources, like this one and this one reach the same conclusion through similar calculations.
