Question

the sum of all 3 digit number whichbare multiple of 7

Answer 1

First we take smaller 3 digit number= 100

Largest 3 digit number= 999

Smaller 3 digit number divisible by 7= 205

Largest 3 digit number=994

So, we take arithmetic sequence (105,112,119........994

a= 205 and d=7

Sequence are

[7(15), 7(16),7(17)....7(142)]

7(15+16+17+.....142)

n(n+1)/2. (Euler summation identity)

7[142(143)/2-14(15/2)]

7[71(143)-7(15)]

70336