SOLUTION: Please help me solve the question: Find the sum of all the multiples of seven between 18 and 711 Thanks =)

Algebra ->  Proportions  -> Lessons -> SOLUTION: Please help me solve the question: Find the sum of all the multiples of seven between 18 and 711 Thanks =)      Log On


   

Question 618264: Please help me solve the question:
Find the sum of all the multiples of seven between 18 and 711
Thanks =)
Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
Please help me solve the question:
Find the sum of all the multiples of seven between 18 and 711
Thanks =)

Since the multiples of 7 that are between 18 and 711 start at 21(7 * 3), and end at 707(7 * 101), then the smallest number is 21, and the largest number is 707 in the series

Additionally, the number of numbers with a difference of 7 between them, which starts at 21 and ends at 707, inclusive, is computed as follows: %28707+-+21+%2B+7%29%2F7, or 693%2F7, or 99

The sum of a series of numbers can be found by applying the following formula:
S%5Bn%5D+=+%28n%2F2%29%28a%5B1%5D+%2B+a%5B2%5D%29, with n being the number of numbers; and a%5B1%5D and a%5B2%5D being the smallest and largest numbers in the series, respectively

S%5B99%5D+=+%2899%2F2%29%2821+%2B+707%29 ---- Substituting 99 for n; 21 for a%5B1%5D and 707 for a%5B2%5D, respectively

S%5B99%5D+=+%2849.5%29%28728%29

highlight_green%28S%5B99%5D+=+36036%29

Send comments and “thank-yous” to “D” at MathMadEzy@aol.com