Question 129

The sum of all the natural numbers between 100 and 1000 which are multiples of 5 is


The natural number between 100 and 1000 are $$105, 110, 115......995$$

It is making an arithmetic series.

Sum of the terms of arithmetic series $$S_n=\dfrac{n(2a+(n-1)d)}{2}$$





Hence, the required sum $$S_n=\dfrac{179(2\times 105+(179-1)\times 5)}{2}$$

$$S_n=\dfrac{179\times(210+178\times 5)}{2}=550\times 179=98450$$

Hence, the required sum $$S_n=98450$$

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