Question

Find the total number of integers between 10 and 1000 that are divisible by 3.

Answer 1

this simply becomes the arithmetic series
12 + 15 + 18 + .... + 999
where a = 12 , d = 3

so how many terms are there ?
termn = a + (n-1)d
999 = 12 + (n-1)(3)
987 = 3m - 3
990 = 3n
n =330

sum = (330/2)(24 + 329(3)) = 166815

or
sum = (n/2)(first + last)
= 165(12+999) = 166815

Answer 2

Thank u