2Using AP, find the sum of all 3-digit natural numbers which are the m

1.	2Using AP, find the sum of all 3-digit natural numbers which are the multiples of 7.
Answer» The first three digit number which is divisible by 7 is 105 and last three digit number which is divisible by 7 is 994. This is an A.P. in whicha= 105, d = 7 and l = 994. Let the number of terms be n . Thentn= 994. nthterm of A.P = tn= a + (n - 1)d. ⇒ 994 = 105 + (n -1)7. ⇒ 889 = 7(n-1) ⇒ n -1 = 127 ∴ n = 128. ∴ There are128 three digit numbers which are divisible by 7.

2Using AP, find the sum of all 3-digit natural numbers which are the multiples of 7.

Answer»

The first three digit number which is divisible by 7 is 105 and last three digit number which is divisible by 7 is 994.

This is an A.P. in whicha= 105, d = 7 and l = 994.

Let the number of terms be n . Thentn= 994.

nthterm of A.P = tn= a + (n - 1)d.

⇒ 994 = 105 + (n -1)7.

⇒ 889 = 7(n-1)

⇒ n -1 = 127

∴ n = 128.

∴ There are128 three digit numbers which are divisible by 7.