Question

Find the sum of all natural numbers between 100 and 1000 which are multiples of 5 or 2.
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Answer 1

The natural numbers lying between 100 and 1000, which are multiples of 5, are 105, 110, … 995.

Here, first term, a = 105 Common difference,

d = 5 Here, a+(n−1)d

= 995 => 105+(n−1)5

=995 => (n−1)5

= 995−105 = 890

=> n−1 = 178

=> n = 179

Sn = n/2[2a+(n−1)d]

∴ Sn = 179/2[2×(105)+(179−1)×(5)]

= 179/2[2(105)+(178)(5)]

= 179[105+(89)5]

= (179)[105+445]

= 179×550 = 98450

Hence, the sum of all natural numbers lying between 100 and 1000, which are multiples of 5, is 98450.