Question

How many numbers from 1 to 500 which are exactly divisible by 7?

Answer 1

First let's find out the first number that is divisible by 7 in 1−500.

7x1=7

So,7 is the first number.

Now, let's find the last number.

71×7=497.

So, 497 is the last number.

Now, the series is 7,14,21,28,...,497

Here , first term , a = 7

Common difference, d = 7

last term , an = 497

Terms , n = ?

An = a+(n-1)d

497 = 7 + (n-1) 7

497-7/7 = n-1

70+1 = n

n = 71

Hope it helps you!

Answer 2

AP = 7 , 14 , 21 ......... 497.



Here,


First term ( a ) = 7


Common difference ( d ) = 7


Tn = 497



a + ( n - 1 ) × d = 497



7 + ( n - 1 ) × 7 = 497



7 + 7n -7 = 497


7n = 497


n = 71



Hence,

71 numbers are divisible by 7 between 1 to 500.