13. How many three digit numbers are divisible by 7?

First three-digit number that is divisible by 7 are; First number = 105 Second number = 105+7 = 112 Third number = 112+7 =119 Therefore, 105, 112, 119, … All are three digit numbers are divisible by 7 and thus, all these are terms of an A.P. having first term as 105 and common difference as 7. As we know, the largest possible three-digit number is 999. When we divide 999 by 7, the remainder will be 5. Therefore, 999-5 = 994 is the maximum possible three-digit number that is divisible by 7. Now the series is as follows. 105, 112, 119, …, 994 Let 994 be the nth term of this A.P. first term, a = 105 common difference, d = 7 an = 994 n = ? As we know, an = a+(n−1)d 994 = 105+(n−1)7 889 = (n−1)7 (n−1) = 127 n = 128 Therefore, 128 three-digit numbers are divisible by 7.