(Sum of multiples of $3$ between $1$ and $100$) $-$ (Sum of multiples of $3$ between $5$ and $95$)

Question

$m$ is the sum of all multiples of $3$ between $1$ and $100$. $n$ is the sum of all multiples of $3$ between $5$ and $95$. what is $m-n$?

Answer 1

If $m$ is the sum of all multiples of $3$ between $1$ and $100$, then that is the sum of all multiples between $1$ and $5$, plus all multiples between $5$ and $95$ and all multiples between $95$ and $100$.

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All multiples between $1$ and $5$ is $3$. The sum of all multiples between $5$ and $95$ is $n$. And the multples between $95$ and $100$ are $96$ and $99$.

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So $m = 3 + n +96 +99 = n + 198$.

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ANd $m -n = (n+198)-n = 198$

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