Question

how many numbers lying between 50 and 1500 are divisible by 3

Answer 1

It is the simple question of maths of class 10 maths so lest do it

First we need to find the first number divisible by three which is 51.

Now the last number divisible by 3 is 1500(we are talking about numbers between 50 and 1500).

Now,
We get 1st term 51 and last term 1500
By the formula of arithematic progression we have,

An = a + (n-1)d.
We need to find n or total numbers but we dont have d so lets find out

The second number divisible by three is 54 ....
d= difference between terms (second term and first term) which is 54 - 51=3.

Now by using above formula

An = a + (n -1 )d
1500 = 51 + ( n -1 )3
1500= 51 + ( 3n - 3) ( multiply 3 in braces)
1500 = 51 - 3 + 3n. (Shift same terms one side)

1500= 48 + 3n
1500 - 48 = 3n
1452 = 3n
1452÷ 3 = n
484 which is the total number of terms we want...