Q. 14.5( 104 Votes )

Find the sum of odd integers from 1 to 2001.

Answer :

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


This sequence forms a Arithmetic Progression


Let the first term be ‘a’ and common difference ‘d’.


Let n be the total number of terms in the series.


Here, first term, a = 1


Common difference, d = 2


If l denotes the last term of the series


Then, l = a + (n – 1) × d


Here, l = 2001


2001 = 1 + (n – 1) × 2


2001 – 1 = (n – 1) × 2


2000/2 = n – 1


1000 + 1 = n


n = 1001


Sum of A.P. =




Sn = 1002001


The sum of odd numbers from 1 to 2001 is 1002001.


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