How many integers between 200 and 500 are divisible by 8?

We are given between 200 and 500, and we have to find how many numbers are divisible by 8.
In this series, the first number, divisible by 8, is 200, and the last number, divisible by 8, is
496.
So, the series of numbers divisible by 8 is 200, 208, 216, 224,..., 496. Here, the first term is 𝑎 = 200
 

The common difference is 𝑑 = 208 − 200
⇒ 𝑑 = 8
And the 𝑛𝑡ℎ term is 𝑎 = 496.
𝑛
This forms an A.P. The formula for an A.P.’s 𝑛𝑡ℎ term is given by
𝑎_n = 𝑎 + (𝑛 − 1)𝑑, where 𝑛 is the total number of terms in the series.
Putting the values in the above equation, we get
496 = 200 + (𝑛 − 1)8
⇒ (𝑛 − 1)8 = 496 − 200
⇒ (𝑛 − 1)8 = 296
⇒ (𝑛 − 1) = 296/8 
⇒ (𝑛 − 1) = 37
⇒ 𝑛 = 37 + 1
⇒ 𝑛 = 38
Hence, 38 numbers between 200 and 500 are divisible by 8.