Question

Show that the sum of all odd integers between 1and1000 which are divisible by 3 is 83667

Answer 1

Answer:

Step-by-step explanation:

All odd integers between 1 and 1000 which are divisible by 3 are given by

3,9,15,21,...................993,999

This is an Arithmetic Progression

Here, First Term a = 3, Common Difference = 9 - 3 = 6

Last Term = l = 999

We Know that, l = a + (n - 1) d

or, 999 = 3 + (n - 1) x 6

or, (n - 1) x 6 = 999 - 3

or, 6(n-1) = 996

or, (n - 1) = 996/ 6 = 166

or, n = 166 + 1 = 167

Sum of the above A.P = Sn = n/2 (a + l)

or, 167/2 (3 + 999)

or, 167/2 x 1002

or, Sn = 83667

Hence, Proved