17. Find the sum of all 3 digit nos. which leaves the same remainder 2

1.	17. Find the sum of all 3 digit nos. which leaves the same remainder 2 when divided by 5.
Answer» Three digit numbers which leave the remainder 2 when divided by 5 are 102, 107, 112,117......, 997. 102, 107, 112,......, 997 is an A.P In this A.P a (first term)= 102 d (Common difference)= 5 I(last term ) = 997 l= an = a + (n – 1) d 997= 102 + (n – 1) × 5 5 (n – 1) = 997 – 102 = 895 n-1= 885/5 (n – 1) = 179 n = 179 +1 n = 180 Sum of all three digit numbers which leaves remainder 2 when divided by 5 Sn = n/2 [a+l] Sn= 180/2 [ 102+ 997] Sn= 90 × 1099 Sn= 98910 Sum of all three digit numbers which leaves remainder 2 when divided by 5 is 98910

17. Find the sum of all 3 digit nos. which leaves the same remainder 2 when divided by 5.

Answer»

Three digit numbers which leave the remainder 2 when divided by 5 are 102, 107, 112,117......, 997.

102, 107, 112,......, 997 is an A.P

In this A.P

a (first term)= 102

d (Common difference)= 5

I(last term ) = 997

l= an = a + (n – 1) d

997= 102 + (n – 1) × 5

5 (n – 1) = 997 – 102 = 895

n-1= 885/5

(n – 1) = 179

n = 179 +1

n = 180

Sum of all three digit numbers which leaves remainder 2 when divided by 5

Sn = n/2 [a+l]

Sn= 180/2 [ 102+ 997]

Sn= 90 × 1099

Sn= 98910

Sum of all three digit numbers which leaves remainder 2 when divided by 5 is 98910