Question

Find the sum of the integers between 2 and 100 which are divisible by 3 ?

Arithmethic Series

Answer 1

`1683`

Explanation:

`"the multiples of 3 between 2 and 100 are"`

`3,6,9, ...... ,99`

`"this is an arithmetic sequence with"`

`a_1=3" and "d=9-6=6-3=3`

`"the number of terms "n=99/3=33`

`•color(white)(x)S_n=n/2[2a+(n-1)d]`

`S_(33)=33/2[(2xx3)+(32xx3)]`

`color(white)(S_(33))=33/2(6+96)`

`color(white)(S_(33))=33/2xx102=33xx51=1683`