How many natural numbers are there between 200 and 500, which are divisible by 7?

Question

Philoid · Accepted Answer

The numbers between 200 and 500 that are divisible by 7 are 203, 210, 217, …, 497.

Here, First term = a = 203

Common difference d = 210 – 203 = 7,

Last term = a_n = 497

Since, n^th term is given by:

a_n = a + (n - 1)d

_{497 = 203 + (n – 1)7}

_{497 – 203 = (n – 1)7}

_{294 = 7n – 7}

_{294 + 7 = 7n}

_{301 = 7n}

_{n = 43}

∴ There are 43 natural nos. between 200 and 500 which are divisible by 7.