Question

Find the sum of first natural 1000 numbers which are not diclvisible by 2 or 5

Answer 1

As it is not divisible by 2 we can consider all the odd numbers and also not divisible by 5 so removing the numbers with units place as 5,

So now if we see in 1 to 100
removing divisible by 2 so n=50
but so removing numbers divisible by 5 so sample space will be n=40

now considering such 1000 numbers it will come at 25 times such 100 numbers

hence our last term will be 2499

so applying the arithmetic sum formula

$s = \frac{n}{2} \times (first \: term \: + \: last \: term) \\ \: \: = \frac{1000}{2} \times (1 + 2499) \\ \: \: = 1250000$