Answer:
All even integers will have a common difference of 2.
AP is 102, 104, 106, …, 998
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
n = 449
By using the formula,
Sum of n terms,
S = n/2 [a + l]
S = 449/2 [102 + 998]
S = 449/2 [1100]
S = 449 [550]
S = 246950
∴ The sum of all even integers between 101 and 999 is 246950.