Question

What will be the sum of all 3-digit even positive numbers?

(a) 247050

(b) 269450

(c) 269350

(d) 269580

I got this question in an international level competition.

My question is from Sum of N Terms of Arithmetic Progression topic in portion Arithmetic Progressions of Mathematics – Class 10

Answer 1

Correct option is (a) 247050

Best explanation: The AP according to the given data will be 100, 102, 104, …, 998

Here a = 100 and d = 2

Tn = a + (n – 1)d = 998

100 + (n – 1)2 = 998

100 + 2n – 2 = 998

2n = 998 – 98

n = 450

We know that, Sn = \(\frac {n}{2}\) (a + l)

Sn = \(\frac {450}{2}\) ((100) + 998)

Sn = 225(100 + 998) = 247050