If we list the multiples of 3 and 7 under 10 the results would look like this: 3, 6, 7, 9. The sum of these multiples is 25. Can you find the sum of the multiples of 3 and 7 under 1000?
+26367 If we list the multiples of 3 and 7 under 10 the results would look like this: 3, 6, 7, 9.
The sum of these multiples is 25.
Can you find the sum of the multiples of 3 and 7 under 1000?
\(\begin{array}{|rcll|} \hline 3,\ 6,\ 9,\ \ldots ,\ 999~ (=3*333) \\ 7,\ 14,\ 21,\ \ldots ,\ 994~ (=7*142) \\ \hline \end{array}\)
\(\begin{array}{|rcll|} \hline \text{sum } &=& \dfrac{3+999}{2}*333 + \dfrac{7+994}{2}*142 \\\\ \text{sum } &=& \dfrac{1002}{2}*333 + \dfrac{1001}{2}*142 \\\\ \text{sum } &=& 166833 + 71071 \\\\ \mathbf{\text{sum }} &=& \mathbf{237904} \\ \hline \end{array}\)
