Question

What will be the sum of all natural numbers lying between 500 and 5000, which are divisible by 17?

(a) 567898

(b) 729810

(c) 765835

(d) 234526

The question was asked by my college director while I was bunking the class.

I'd like to ask this question from Sum of N Terms of Arithmetic Progression in division Arithmetic Progressions of Mathematics – Class 10

Answer 1

Right choice is (b) 729810

To elaborate: The AP according to the given data will be 510, 527, 544, …, 4998

Here a = 510 and d = 17

Tn = a + (n – 1)d = 4998

510 + (n – 1)17 = 4998

510 + 17n – 17 = 4998

17n = 4505

n = 265

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

Sn = \(\frac {265}{2}\) ((510) + 4998)

Sn = 132.5(5508) = 729810