Question

Find the sum of all numbers divisible by 6 in between 100 and 400:

• A. 12,550
• B. 12,450
• C. 11,450
• D. 11,550

Hint:

To find the sum of a series of numbers, use the formula for the sum of an arithmetic series: \(S = \frac{n}{2} \times (a + l)\), where \(n\) is the number of terms, \(a\) is the first term, and \(l\) is the last term.

Answer 1

The Correct Option is B

The numbers divisible by 6 between 100 and 400 are 102, 108, 114, ..., 396. This is an arithmetic series where the first term is 102, the common difference is 6, and the last term is 396. The number of terms can be found by using the formula for the nth term of an arithmetic series: \[ n = \frac{396 - 102}{6} + 1 = 50 \] The sum of an arithmetic series is given by: \[ S = \frac{n}{2} \times (a + l) = \frac{50}{2} \times (102 + 396) = 12,450 \]
Therefore, the correct answer is "12,450."