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alexira [117]
3 years ago
6

What is the sum of the multiples of 6 between 6 and 999?

Mathematics
1 answer:
riadik2000 [5.3K]3 years ago
8 0
Your method is completely correct. The first term will be 6 and each subsequent term can be obtained by adding 6 to the previous one, meaning the common difference is 6. The number of terms is given by the highest number that is divisible by 6 and dividing it by 6; that is 996/6 = 166
Then we simply apply the formula for arithmetic sequence sum:
S = n/2 [2a₁ + (n - 1)d]
S = 166/2 [ 2(6) + (166 - 1)6]
S = 83,166
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Step-by-step explanation:

First, you need to find the amount of weeks Pedro spent with his friend. The statement indicates that he spent two weeks more with his friend than with his uncle which means that you have to add the number of weeks he spent with his uncle plus 2, which you can show in a number line:

       3\frac{1}{2}                   2

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1       2       3       4       5       6       7       8       9       10        

3\frac{1}{2}+2=5\frac{1}{2}

Now, you can find the and answer by adding up the number of weeks he spent with his uncle plus the weeks he spent with his friend:

       3\frac{1}{2}                                   5\frac{1}{2}

__________________________________

1       2       3       4       5       6       7       8       9       10  

3\frac{1}{2} + 5\frac{1}{2}=9

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