Question

find the sum of all 3 digit number which leaves reminder 3 when divided 5​

Answer 1

Three digit numbers which leave the remainder 3 when divided by 5 are 103, 108, 113,......., 998.

103, 108, 113,......, 998 is an A.P

First term of the A.P, a = 103

Common different of the A.P, d = 5

Let 998 be the nth term of the A.P.

an = a + (n – 1) d

∴ 103 + (n – 1) × 5 = 998

⇒ 5 (n – 1) = 998 – 103 = 895  

⇒ (n – 1) = 179

⇒  n = 180

Sum of all three digit numbers which leaves remainder 3 when divided by 5

Answer 2

103,108,113,118,—————,998
L=103 +(n-1)5=998
So n=180
S(180)=90(103+998)
90* 1101
= 99090