Question

how many numbers from 1001 to 2000 divisible by 4​

Answer 1

Answer:

Numbers divisible by 4 :

1004, 1008,...............2000

Step-by-step explanation:

a = 1004

d = 4

Tn = 2000

$Tn = a + (n - 1)d \\ 2000 = 1004 + (n - 1)4 \\ 2000 = 1004 + 4n - 4 \\ 2000 = 4n + 1000 \\ 2000 - 1000 = 4n \\ 1000 = 4n \\ \frac{1000}{4} = n \\ 250 = n$

So, there are totally 250 numbers between 1001 and 2000 which are divisible by 4.

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Answer 2

Answer:

250 numbers

Explanation:

The smallest Number which is divisible by 4 from 1001 and 2000.

= 1000 + 4 = 1004

The largest Number which is divisible by 4 from 1001 and 2000.

= 2000

If we know, at which position 200 will lie, then we could find the number of the multiples of 4 from 1001 and 2000

The nth term of an AP = f + ( n - 1 )d

f = First term

n = position of the term

d = comman difference between the terms.

⟹ 2000 = 1004 ( n - 1 )(4)

⟹ 2000 - 1004 = ( n - 1 )(4)

⟹ 996 = ( n - 1 )(4)

⟹ 249 = ( n - 1 )

⟹ 249 + 1 = n

⟹ 250 = n

Position of the last term = Number of terms

So, there are 250 numbers from 1001 and 2000 that are divisible by 4.