Question

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

Answer 1

Hint: The integers between 200 and 500 which are divisible by 8 are: 208,216,224…………496. These numbers are in A.P, use the property of A.P to find the total number of integers. Use the equation $L = a + (n - 1)d$, where, a is the first term, n is the total number of terms, d is the common difference and L is the last term of a A.P.

Complete step-by-step answer:
Given to find the integers between 200 and 500 which are divisible by 8.
Therefore, the integers between 200 and 500 which are divisible by 8 are: 208,216,224…………496.
These numbers are in A.P., the first term is 208 and the last term is 496.
Last term in an A.P. is $L = a + (n - 1)d$.
 Here, a is the first term, n is the total no. of terms, d is the common difference and L is the last term.
Now, $a = 208,d = 8,L = 496$.
Put in equation $L = a + (n - 1)d$, we get
$
  496 = 208 + (n - 1)8 \\
  288 = (n - 1)8 \\
  n - 1 = 36 \\
  n = 37 \\
 $
Therefore, the no. of integers between 200 and 500 which are divisible by 8 are 37.

Note: Whenever such type of questions appears first write the numbers between the given range which are divisible by 8, (No need of writing all numbers, just write two- three no. at the beginning and the last no. which is divisible in the given range), as mentioned in the solution these numbers form A.P., use the formula, $L = a + (n - 1)d$, put all the known values and find the unknown value.