Question

Find the sum of numbers between 200 and 300,which is multiple of 3

Answer 1

here's your answer dear...

Answer 2

Given,

• Numbers between 200 and 300

To find,

• Sum of numbers between 200 and 300, which is a multiple of 3.

Solution,

The sum of numbers between 200 and 300, which is a multiple of 3 is 8217.

The A.P. series of the numbers between 200 and 300 which are divisible by 3 is 201, 204,_____297.

The first term of the AP 'a' = 201

common difference 'd' = 3

The last term '$a_{n}$' = 297

For finding the number of terms 'n', we will use the following formula,

                    $a_{n} = a + (n-1)d$

                 297 =  201 + (n-1)3

          297-201 =3n-3

                  96  = 3n-3

                96+3 = 3n

                 99/3 = n

                    33 = n

Now, for finding the sum of 33 numbers between 200 and 300 which is a multiple of 3, we will use the following formula,

                   $S_{n} = n/2 (a+a_n)$

                  $S_{33}$ = 33/2 (201 + 297)

                  $S_{33}$ =  33/2 * 498

                        = 249 * 33

              $S_{33}$     = 8217

∴ The sum of 33 terms between 200 and 300 is 8217.

Hence, the sum of numbers between 200 and 300, which is a multiple of 3 is 8217.