74.Find the sum of all three-digit numbers whichleaves remainder 2, wh

1.	74.Find the sum of all three-digit numbers whichleaves remainder 2, when divided by 3.
Answer» All three digit numbers when divided by 3 leave remainder 2 will form AP series. The series will be of the form: 101, 104, 107.....995, 998 a = 101, d = 104 - 101 = 3 Total number of terms 998 = 101 + (n-1)3998 = 101 + 3n - 33n = 1001 - 101n = 900/3 = 300 Sum of n terms of an AP isSn = n/2(first term + last term) Then, sum of given series = 300/2(101 + 998)= 150(1099)= 164850

74.Find the sum of all three-digit numbers whichleaves remainder 2, when divided by 3.

Answer»

All three digit numbers when divided by 3 leave remainder 2 will form AP series.

The series will be of the form: 101, 104, 107.....995, 998

a = 101, d = 104 - 101 = 3

Total number of terms 998 = 101 + (n-1)3998 = 101 + 3n - 33n = 1001 - 101n = 900/3 = 300

Sum of n terms of an AP isSn = n/2(first term + last term)

Then, sum of given series = 300/2(101 + 998)= 150(1099)= 164850