Question

Find the sum of numbers between 1 to 200 which when divided by either 5 or 7 leaves remainder of 2 ?

Answer 1

Numbers which are divided by 5, gives remainder 2:
2, 7,12,17 .......... 197
Series is in AP with common difference 5.
Last term = 197
a + (n-1)*d = 197
2 + (n -1)*5 = 197
n = 38
Sum = [n*(first term + Last term)/2]
Sum = 19 *(2+197) = 3781.
The numbers which are divided by 7, gives remainder 2:
2, 9, 16, 23 ............... 198
L = 198
a + (n-1)*d = 198
2 + (n-1)*7 = 198
n = 27
Sum = [27*(2+198)/2]= 2700.
Required sum = 3781 + 2700 - 2 = 6479
** 2 has been added twice so we will deduct it from final result.