Question

Find the sum of odd integers from 1 to 2001.

Answer 1

The odd integers from 1- 2001are 1,3,5,……1999,2001.

The above sequence forms an A.P.

Here, the first term and common difference is given by,

a=1 d=2

Let n be the total number of odd integers between 1 to 2001.

The formula to find terms in an A.P. is given by,

T n =a+( n−1 )d

Substitute the values of T n , a, and d as 2001, 1, 2 in the above expression.

2001=1+( n−1 )×2 2001=1+2n−2 2n−2=2000 2n=2002

Further simplify the above expression.

n=1001

The formula for the sum of n terms in an A.P. is given by,

S n = n 2 [ 2a+( n−1 )d ]

Substitute the values in the above expression.

S n = 1001 2 [ 2×1+( 1001−1 )×2 ] = 1001 2 [ 2+1000×2 ] = 1001 2 ×[ 2+2000 ] = 1001 2 ×2002

Further simplify the above expression.

S n =1001×1001 = ( 1001 ) 2 =1002001

Thus, the sum of the odd integers from 1 to 2001 is 1002001.