Question

Find the sum of odd integers from 1 to 2001.

Answer 1

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Answer 2

10,02,001

The odd integers from 1 to 2001 are in the form of an AP.

The First Term Of This AP (a) = 1

The Common Difference Of This AP (d) = 2

To Find:

The sum of odd integers from 1 to 2001.

Calculating:

First let us find the nth term of this AP.

To find the nth term of an AP we use the formula:

an = a + (n - 1) d

Substituting all the values we know into this formula we get:

2001 = 1 + (n - 1)(2)

Taking 1 to the other side of the equation we get:

2001 - 1 = (n - 1)(2)

2000 = (n - 1)(2)

Taking 2 to the other side of the equation we get:

2000 / 2 = n - 1

1000 = n - 1

Taking - 1 into the other side of the equation we get:

n = 1000 + 1

n = 1001

Therefore, the nth term of the AP is 1001.

Now we need to calculate the sum of odd integers from 1 to 2001. So we use the formula to calculate the sum of n terms.

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

Sn  = n/2(2a + (n - 1) (d)

Substituting all the values known to us into this formula we get:

Sn = 1001/2 (2 x 1 + (1001 - 1) (2))

Sn = 1001/2 (2 + ((1000) (2))

Sn = 1001/2 (2 + 2000)

Sn = 1001/2 (2002)

Sn = 1001 x 1001

Sn = 10,02,001

Hence, the sum of odd integers from 1 to 2001 is 10,02,001.