How many numbers lie between 10 and 300, which divided by 4 leave a re

1.	How many numbers lie between 10 and 300, which divided by 4 leave a remainder 3?
Answer» Here, the first number is 11, which divided by 4 leave remainder 3 between 10 and 300. And the next number is 15 and the next is 19 Last term before 300 is 299, which divided by 4 leave remainder 3. So, the list is 11, 15, 19, …, 299 Clearly, This is an AP With first term, a = 11 Common difference, d = 15 - 11 = 4 Last term, a_n = 299 Using the nth term formula a_n = a + (n - 1)d 299 = 11 + (n - 1) (- 4) 299 - 11 = (n - 1) (- 4) 288 = (n - 1) (- 4) n - 1 = 72 n = 73 So there are 73 numbers between 10 and 300 which leaves 3 as remainder when divided by 4.

How many numbers lie between 10 and 300, which divided by 4 leave a remainder 3?

Answer»

Here, the first number is 11, which divided by 4 leave remainder 3 between 10 and 300.

And the next number is 15 and the next is 19

Last term before 300 is 299, which divided by 4 leave remainder 3.

So, the list is

11, 15, 19, …, 299

Clearly, This is an AP

With first term, a = 11

Common difference, d = 15 - 11 = 4

Last term, a_n = 299

Using the nth term formula

a_n = a + (n - 1)d

299 = 11 + (n - 1) (- 4)

299 - 11 = (n - 1) (- 4)

288 = (n - 1) (- 4)

n - 1 = 72

n = 73

So there are 73 numbers between 10 and 300 which leaves 3 as remainder when divided by 4.