Question

How many numbers are completely divisible by 225 betwer 1000 and 5000?

Answer 1

There are 18 numbers between 1000 and 5000 which is exactly divisible by 225

Answer 2

Answer:

there are 18 numbers exactly divisible

Step-by-step explanation:

THE STEPS:

Step-1 : Find the Smallest number which is greater than 1000 and is completely divisible by 225.

Here, that first number is 1125.

Step-2: Divide the last number in the interval, i.e. 5000 by 225 and find the remainder.

Now Subtract the remainder obtained from 5000 to get the last number which is divisible by 225 in the given interval.

Here, the last number is 4950.

Now, the sequence will be of the form: 1125 , 1350(1125+225) , ……….. , 4950.

Now, apply the Arithmetic Progression (A.P.) formula:

a (first term) = 1125

d (common difference, i.e. (Second Term - First Term)) = 225

l (last term) = 4950

Step -3 : Now, find the number of terms in the Series by using the formula:

T(n) = a + (n-1)d ,where T(n) is the nth term

4950 = 1125 + (n-1)225

n = 18 (On Solving)

Therefore, 18 numbers between 1000 and 5000 which are divisible by 225.

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