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Sum of N Terms of an AP

Question

Find the sum of all three-digit natural numbers which leave a remainder $2$ when they are divided by $3$ .

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Solution

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$104, 107, . . ., 998 998 = 104 + (n - 1) \times 3 \Rightarrow \frac{894}{3} = n \cdot 1 \Rightarrow n = 298 + 1 = 299$
Sum $= \frac{299}{2} (104 + 998)$
$= 164749.$

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