Question

Find the sum of all natural numbers between 100 & 1000, which are multiples of 5​

Answer 1

98450

The natural numbers between 100 and 1000 which are a multiple of 5 is in the form of an AP.

First term of this AP (a) = 105

Common Difference of this AP (d) = 5

To Find:

The sum of all natural numbers between 100 and 1000.

Calculating:

First we need to calculate the nth term of the AP.

For calculating the nth term of an AP we use the formula:

an = a + (n - 1) d

Substituting all the values that are known to us in this formula we get:

995 = 105 + (n - 1) (5)

995 - 105 = (n - 1) (5)

890 = (n - 1) (5)

890 / 5 = n - 1

178 = n - 1

n = 178 + 1

n = 179

Therefore, the n th term of the AP is 179.

Now, we have to find the sum of all natural numbers between 100 and 1000 for this we use the formula to calculate the sum of n terms of an AP.

The formula that is used to calculate the sum of n terms of an AP:

Sn = n/2(2a + (n - 1) (d)

Substituting the values which are known to us in this formula we get:

Sn = 179/2 (2 x 105 + (179 - 1) (5)

Sn = 179/2 (210 + (178) (5) )

Sn = 179/2 (210 + 890)

Sn = 179/2 (1100)

Sn = 179 x 550

Sn = 98450

Hence, the sum of all natural numbers between 100 and 1000 which are multiples of 5 is 98450.