Question

find the sum of all three digit numbers which when divided by 11 leave remainder 5

Answer 1

The sum of all 3 digit numbers which when divided by 11 leaves remainder 5 ​is equal to 45059.

The numbers that will leave a remainder of 5 on dividing by 11 must be of the form 11n + 5, where n is a natural number.

for the number to be a 3 digit number n must be greater than 9 and lest than 90.

So we get an AP with 104 as the first term, common difference equal to 11 and 995 as the last term.

Sum=104+115+126+...............+995(total 82 terms)

Sum of AP = no. of terms ×(first term +last term)/2

Evaluating the above expression , we get our sum to be 45059