To solve this problem, we need to find the sum of multiples of 6 between 6 and 999. Let's break it down step by step to double-check your answer:
1. First, calculate the number of terms: To find the number of terms in a sequence of multiples, we can use the formula: number of terms = (last term - first term) / common difference + 1. In this case, the first term is 6, the last term is 999, and the common difference is 6. Plugging these values into the formula, we get: (999 - 6) / 6 + 1 = 166 + 1 = 167.
2. Next, calculate the sum: To find the sum of an arithmetic sequence, we can use the formula: sum = (number of terms / 2) * (first term + last term). Plugging in the values we found, we have: sum = (167 / 2) * (6 + 999) = 83.5 * 1005 = 83767.5.
Now, let's compare the result with your answer:
- Your answer: 83166
- Correct answer: 83767.5
It seems that your calculated sum of 83166 is slightly different from the correct answer of 83767.5. This discrepancy might be due to a rounding error or missing a fraction in the calculation. Therefore, your answer is indeed incorrect, and the correct sum of the multiples of 6 between 6 and 999 is 83767.5, rounded to 82665 according to your answer key.