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 $$S_n=\dfrac{n(2a+(n-1)d)}{2}$$
$$t_n=a+(n-1)d$$
$$995=105+(n-1)5$$
$$n-1=\dfrac{995-105}{5}=178$$
$$n=178+1=179$$
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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