There are 27 numbers between 10 and 200 that are exactly divisible by 7.
The reference states that the numbers between 10 and 200 divisible by 7 are: 14, 21, 28, ..., 196. To find how many numbers are in this sequence, we need to determine the first and last number in the range that's divisible by 7 and then apply some basic arithmetic.
Here’s how to determine the count:
- Finding the First Multiple: The first multiple of 7 greater than 10 is 14 (7 * 2).
- Finding the Last Multiple: The last multiple of 7 less than 200 is 196 (7 * 28).
- Creating the Arithmetic Sequence: The sequence of multiples of 7 forms an arithmetic progression: 14, 21, 28, ..., 196. The common difference is 7.
- Calculating the Number of Terms:
- We can think of the sequence as 7 2, 7 3, 7 4, ..., 7 28
- To find the number of terms, we can find the difference in the multipliers of 7 which is (28-2) = 26
- Add 1 to include the first multiple and we get 27
- Alternatively, using the arithmetic sequence formula: nth term = first term + (n-1) common difference. So, 196 = 14 + (n-1) 7. Solving for n, we get (196-14)/7 + 1 = 26 +1 = 27.
Therefore, there are 27 numbers between 10 and 200 that are exactly divisible by 7.
