(1) what is the sum of all 3 digit numbers that leave a remainder of 2 when divided by 3 ?
(2) How many 3 digit positive integers exist that when divided by 7 leave a remainder of 5 ?
1) The least number is $\displaystyle 101=3\cdot 33+2$
The greatest number is $\displaystyle 998=3\cdot 332+2$
You have to calculate $\displaystyle \sum_{k=33}^{332}(3k+2)$
2) The least number is $\displaystyle 103=7\cdot 14+5$
The greatest number is $\displaystyle 999=7\cdot 142+5$
How many numbers are from 14 to 142?