question_answer

Find how many integers between 200 and 500 are divisible by 8?

Answer:

Smallest divisible no. (by 8) in given range \[=208\]

Last divisible no. (by 8) in range \[=496\]

So, \[a=208,\,\,d=8,\,\,n=?,\,\,{{a}_{n}}=496\]

\[{{a}_{n}}=a+(n-1)d\]

\[=208+(n-1)8=496\]

\[\Rightarrow \]   \[8n+208-8=496\]

or                        \[8n=496-200=296\]

\[n=\frac{296}{8}=37\]

So number of terms between 200 and 500 divisible by 8 are 37.