SOLUTION: what is sum of all multiples of 6 that are strictly between 3138 and 51804? please help i my exam is 05/07/09 so it is urgent please help!!!!!!

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Question 194494: what is sum of all multiples of 6 that are strictly between 3138 and 51804?
please help i my exam is 05/07/09 so it is urgent please help!!!!!!

Answer by Edwin McCravy(20066) About Me  (Show Source):
You can put this solution on YOUR website!
The multiples of 6 form an arithmetic sequence with common
difference, d = 6.

3138 and 51804 are both multiples of 6.  However the fact that

it says "strictly between 3138 and 51804", we must begin with

the first multiple of 6 larger than than 3138, which is 3144.

Also we must end with largest multiple of 6 less than 51804,

which is 51798.  So,

a%5B1%5D=3144, a%5Bn%5D=51798

The formula for the nth term is

a%5Bn%5D=a%5B1%5D%2B%28n-1%29d

51798=3144%2B%28n-1%296

51798=3144%2B6%28n-1%29

51798=3144%2B6n-6

51798=3138%2B6n

51798=3138%2B6n

48660=6n

8110=n

The formula for the sum of the n terms 
of an arithmetic sequence is

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

S%5B8110%5D=8110%283144%2B51798%29%2F2

S%5B8110%5D=8110%2854942%29%2F2

S%5B8110%5D=8110%2854942%29%2F2

S%5B8110%5D=222789810

Edwin