Question

find how many integers between 200 and 500 are dovisible by 8

Answer 1

Heya user,

A∈[500/8] = [62]
B∈[200/8] = [25]

=>A∪B = [62] - [25] = 37..

Another Method is... 
The 1st term is a = 208. c.d. =8 And last term = 496..
.'. No. of terms can be taken ot as: 208+(n-1)8 = 496
=> (n-1)8 = 288
=> (n-1) = 36
=> n = No. of terms = 36+1 = 37

Answer 2

First term between 200 and 500 divisible by 8  is 208, and the last term is 496

First term, a = 208

Common difference (d) = 8

an = a + (n – 1) d = 496

⇒ 208 + (n – 1) 8 = 496

⇒ (n – 1) 8 = 288

⇒ n – 1 = 36

⇒ n = 37

Hence, there are 37 integers between 200 and  500 which are divisible by 8.