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Black_prince [1.1K]
3 years ago
12

Find the sum of all the integers from 1 to 100 inclusive that are not Multiples of 7.

Mathematics
1 answer:
Nonamiya [84]3 years ago
5 0

Step-by-step explanation:

\text{Denote The sum of all the integers from 1 to 100 inclusive that are NOT multiples of 7 as } S.

\text{Denote The sum of all the integers from 1 to 100 inclusive that are multiples of 7 as } P.

\text{Denote The sum of all the integers from 1 to 100 inclusive as } Q.

Then

\begin{align}S&=Q-P\\&=\frac{100(100+1)}{2}-(7+2\cdot7+\ldots+14\cdot7)\\&=\frac{100(100+1)}{2}-7\cdot\frac{14(14+1)}{2}\\&=4315\end{align}

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