Question

how many natural number are there between 200 and 500 which are divisible by 7​

Answer 1

Answer:

203 is the first natural no. divisible by 7 b't 200&500

next no. s will be

210,217,......497

here a sequence is developed in AP is that

203 ,210,217,......497

a=203

d=7

nth term =497

nth term =a+(n-1)d

497=203+(n-1)7

n-1=42

n=43

So ,43 natural no.s lie b't 200&500 which is divisible by 7 .

Answer 2

First natural number that is divisible by 7 that is between 200 and 500

= 203

Last number that is divisible by 7 that is between 200 and 500

= 497

Common difference of the AP:

= 7

The formula used to find the nth term of the Arithmetic Progression:

an = a + (n - 1)d

Substituting all the values known to us in this formula we get:

497 = 203 + (n-1)7

Taking 203 to the other side and multiplying (n - 1) x 7 we get:

497 - 203 = 7n - 7

294 + 7 = 7n

301/7 = n

n = 43

Therefore, 43 numbers are divisible by 7 between 200 and 500.