SOLUTION: How many numbers between 5 and 200 are divisible by 3? Insert four arithmetic means between -1 and 14

Question 1188228: How many numbers between 5 and 200 are divisible by 3?
Insert four arithmetic means between -1 and 14
Answer by Edwin McCravy(20056) (Show Source): You can put this solution on YOUR website!
How many numbers between 5 and 200 are divisible by 3

The first one is 6 and the last one is 198 because
200/3 = 66.66... and 66x3 = 198, they go 

6, 9, 12, ..., 198

Divide them all by 3

2, 3,  4, ..., 66

Subtract 1 from them all

1, 2,  3, ..., 65

So there are 65 of them.

Insert four arithmetic means between -1 and 14

-1, -1+d, -1+2d, -1+3d, -1+4d, -1+5d = 14
                                  5d = 15
                                   d = 3

-1, -1+(3), -1+2(3), -1+3(3), -1+4(3), -1+5(3) = 14

-1, 2, -1+6, -1+9, -1+12, -1+15 = 14

-1, 2, 5, 8, 11, 14 = 14

So the four arithmetic means are 2, 5, 8, and 11.

Edwin

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