Answer:
The odd numbers between 1 and 1000 divisible by 3 are 3, 9, 15,…,999
Number of terms be ‘n’, so the nth term is 999
a = 3, d = 9-3 = 6, an = 999
an = a + (n-1)d
999 = 3 + (n-1)6
999 = 3 + 6n – 6
6n = 999 + 6 – 3
6n = 1002
n = 1002/6
n = 167
By using the formula,
Sum of n terms,
S = n/2 [a + l]
S = 167/2 [3 + 999]
S = 167/2 [1002]
S = 167 [501]
S = 83667
∴ The sum of all odd integers between 1 and 1000 which are divisible by 3 is 83667.
Thus, proved.