Question

find the sum of all positive integers less than 200 which when divided by 7 leaves remainder as 3

Answer 1

The number less than 200 which when divided by 7 leaves remainder as 3:-

      10 + 17 + 24 +.......................... + 199

a= 10, d= 7 , tn =199, n=?  sum of n =?

tn = a + (n-1) d

199 = 10 + (n-1) 7

199 - 10 = (n-1) 7

189  = (n-1) 7

n-1  = 189/7

n  = 27 + 1

n = 28

Sum of the number = n/2 (2 a + (n-1) d)

                                = 28/2 (2 x 10+ (28-1) 7)

                                 = 14 ( 20 + 189)

                                  = 14 x  209

                                 = 2926