Question

integers from 11to1000 which are divisible by 3

Answer 1

12, 15, 18,............ 999

a = 12

d = 3

L = 999

=> a + (n-1)d = 999

=> 12 + (n-1) 3 = 999

=> (n-1) 3 = 987

=> n-1 = 329

=> n = 330

Number of integers between 11 and 1000, that are divisible by 3 = 330

Answer 2

333....1 - 9 -> 3 , 6 , 9 => Three nos in this range = 3

10 - 99 -> 12, 15, 18 …..,99 => Thirty nos in this range { we can get the value of n by using the nth term formula i.e [a + (n-1) *  d] } = 30

100–999 -> 102,105,…..,999 => Three hundred nos in this range = 300

 total numbers between 1 and 1000 divisible by 3 = 3 + 30 + 300 = 333.