Question

Find the sum of all numbers between 100 and 400 which are exactly divisible by 3

Answer 1

Sn=102+105+108+..................+399

a=105, d=3, Tn=l=399, n=?, Sn=?

a+(n-1)d=Tn

102+(n-1)3=399

102+3n-3=399

3n+99=399

3n=399-99

3n=300

n=300/3

n=100

No. of terms=100

Sn=n(a+l)/2

=100(102+399)/2

=100(501)/2

=50100/2

=25025

Sum of all nos. between 100 and 400 that are divisible by 3=25025