Question

how many natural numbers between 200 and 400 which are divisible by 4or5or8or 10​

Answer 1

Answer:

Numbers which are divisible by 4 or 5 or 8 or 10 form AP respectively

1). AP formed in case of 4

200 , 204 , 208 , ... , 400

first term, a = 200  , d = 4 and last term = 400

we know that,

$a_n=a+(n-1)d$

$400=200+(n-1)4$

$(n-1)4=200$

$n-1=50$

$n=51$

Therefore, Between 200 and 400,  51 numbers are divisible by 4.

2). AP formed in case of 5

200 , 205 , 210 , ... , 400

first term, a = 200  , d = 5 and last term = 400

we know that,

$a_n=a+(n-1)d$

$400=200+(n-1)5$

$(n-1)5=200$

$n-1=40$

$n=41$

Therefore, Between 200 and 400 , 41 numbers are divisible by 5.

3). AP formed in case of 8

200 , 205 , 210 , ... , 400

first term, a = 200  , d = 8 and last term = 400

we know that,

$a_n=a+(n-1)d$

$400=200+(n-1)8$

$(n-1)8=200$

$n-1=25$

$n=26$

Therefore, Between 200 and 400 , 26 numbers are divisible by 8.

4). AP formed in case of 10

200 , 205 , 210 , ... , 400

first term, a = 200  , d = 10 and last term = 400

we know that,

$a_n=a+(n-1)d$

$400=200+(n-1)10$

$(n-1)10=200$

$n-1=20$

$n=21$

Therefore, Between 200 and 400 , 21 numbers are divisible by 10.