Question

find the sum of all natural numbers between 101 and 999 which are divisible by both 2 and 5

Answer 1

2  x  5 = 10

thr natural number which can be divided by both 2 and 5 (i.e. 10). =

110, 120, 130, ......... ... . ...........,  990

 a                   d = 10                    an

an  = a + (n - 1)d

990 = 110 + (n-1)10

880 = (n-1)10

88 = n-1

n = 89

sum of 1st n term of  AP = na + [n(n-1)]/2  x d

= (89 x 110) + [ 89(89-1)]/2  x 10

= 9790 + 7832/2 x 10

= 9790 + 3916 x 10

= 9790 + 39160

= 48950