Question

Find the sum of all three digit no which are divisible by 11

Answer 1

here the AP is
110,121............990
Tn = 990, a = 110, d = 11
Tn = a + (n - 1) × d
990 = 110 + (n - 1) × 11
990 - 110 / 11 = n-1
880 / 11 = n-1
80 = n-1
n = 80 + 1
n = 81

Sn = n/2 [ T1 + Tn ]
S81 = 81 / 2 [ 110 + 990 ]
S81 = 81 /2 × 1100
S81 = 81 × 550
S81 = 44550

therefore the sum of all three digit no. which are divisible by 11 is 44550