Question

find the sum of integers between 200 and 500 which leaves reminder 5 in each case when divided by 8
please help​

Answer 1

Answer:

12708

Step-by-step explanation:

Between 200 and 500 :

  First number divisible by 8 = 208, so the number that will leave a remainder of 5 when divided by 8 should be 208 + 5 = 213.

 Last number divisible by 8 = 496, so the number that will leave a remainder of 5 when divided by 8 should be 496 + 5 = 501, but this greater than 500, so the last required number is 488 + 5 = 493.

Here, this forms an AP :

  a = first term = 213

  last term = l = 493

For n:

 493 = a + ( n - 1 )d

⇒ 493 = 213 + ( n - 1 )8

⇒ 280 = ( n - 1 )8

⇒ 36 = n

         Hence, required sum is :

⇒ (n/2) ( a + l )

⇒ (36/2) ( 493 + 213 )

⇒ 18( 706 )

⇒ 12708

   Required sum is 12708