SOLUTION: Please help. The sum of the integers between 10 and 65, inclusive, which are divisible by 2 and 3 is _____ Thanks in advance!

Algebra ->  Sequences-and-series -> SOLUTION: Please help. The sum of the integers between 10 and 65, inclusive, which are divisible by 2 and 3 is _____ Thanks in advance!      Log On


   

Question 995915: Please help.
The sum of the integers between 10 and 65, inclusive, which are divisible by 2 and 3 is _____
Thanks in advance!
Answer by ikleyn(52787) About Me  (Show Source):
You can put this solution on YOUR website!
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These integers are  12, 18, 24, . . . , 60.

It is arithmetic progression with the first term  12  and the difference  6;  the last term is  60. The number of the terms is %2860-12%29%2F6+%2B+1 = 48%2F6+%2B+1 = 8 + 1 = 9.

Use the formula for the sum of arithmetic progression

S = %28%28a%5B1%5D%2Ba%5Bn%5D%29%2F2%29%2An

(see the lesson  Arithmetic progressions  in this site).  It gives

S = %2812+%2B+60%29%2F2%2A9 = 72%2F2%2A9 = 36*9 = 324.