How many numbers between 100 and 300 are divisible by 7?

Correct option is B

Given: 

To find total numbers between 100 and 300 are divisible by 7.

Concept Used:

The general formula for the n-th term of an arithmetic sequence is:

​$$a_n = a_1 + (n - 1) \times d$$ 

where $$a_1$$​ is the first term, d is the common difference, and $$a_n$$​ is the n-th term.

Solution:

105 is the smallest multiple of 7 that is greater than or equal to 100.

294 is the largest multiple of 7 that is less than or equal to 300.

The multiples of 7 between 105 and 294 form an arithmetic sequence with the first term 105, the common difference 7, and the last term 294.

when $$a_n = 294$$​

Substituting the values into the formula:

$$294 = 105 + (n - 1) \times 7$$ 

$$294 - 105 = (n - 1) \times 7$$

$$189 = (n - 1) \times 7$$ 

$$n - 1 = \frac{189}{7} = 27$$ 

$$n = 28$$ 

​So, there are 28 multiples of 7 between 100 and 300.​