The sum of all odd integers between 1 and 1000 which are divisible by 3 is **83667.**

**Given : **

Odd integers between 1 and 1000 which are divisible by 3 are **3, 9 ,15 ..........999.**

Here,** a = 3 , d = 9 - 3 = 6 , a**_{n} ,(l) = 999

**By using the formula ,a**_{n} = a + (n - 1)d

999 = 3 + (n - 1)6

999 = 3 + 6n - 6

999 = 6n - 3

999 + 3 = 6n

1002 = 6n

n = 1002/6

n = 167

**By using the formula ,Sum of nth terms , S**_{n} = n/2 [a + l]

S_{167} = 167/2 [3 + 999]

S_{167} = 167/2 × 1002

S_{167} = 167 (501)

S_{167} = 83667

**Hence Proved that the sum of all odd integers between 1 and 1000 which are divisible by 3 is 83667.**