Find how many integers between 200 and 500 are divisible by 8. (CBSE 2017)

The integers between 200 and 500 divisible by 8 are 208, 216, 224,…,496.

This forms an AP with first term = a = 208

and common difference = d = 8

Last term is 496.

Now, number of terms in this AP are given as:

496 = a + (n – 1)d

⇒ 496 = 208 + (n - 1)8

⇒ 496 – 208 = 8n – 8

⇒ 288 = 8n - 8

⇒ 288 + 8 = 8n

⇒ 296 = 8n

⇒ n = 37

There are 37 integers between 200 and 500 that are divisible by 8.