We know that all even integers will have a common difference of 2.
So, AP is 102, 104, 106, …, 998
We know, a = 102, d = 104 – 102 = 2, an = 998
By using the formula,
an = a + (n - 1)d
998 = 102 + (n - 1)2
998 = 102 + 2n – 2
2n = 998 – 102 + 2
2n = 898
n = 898/2
= 449
By using the formula,
Sum of n terms, S = n/2 [a + l]
= 449/2 [102 + 998]
= 449/2 [1100]
= 449 [550]
= 246950
∴ The sum of all even integers between 101 and 999 is 246950.
