Question

Find the sum of no. Of integers between 100 and 200 that are not divisible by 6

Answer 1

Let's first consider the numbers between 100 and 200 that are divisible by 6,

They are : 102,108,114...........198.

They form an AP, where,

a=102

d=6

l=198

l=a+(n-1)*d

∴198=102+(n-1)*6

∴96=(n-1)*6

∴n=17

Sum of these numbers=n/2(a+l)

                                     =17/2(102+198)

                                     =17*150

                                     =2550

Consider all nos. between 100 and 200,

They are : 101,102,103..........199.

They form an AP where,

a=101

d=1

l=199

n=99

∴Their sum = n/2(a+l)

                   =99/2(101+199)

                   =99*150

                   =14850

Now,

Sum of integers between 100 and 200 that are not divisible by 6

=14850-2550

=12300