Q. 14.5( 104 Votes )
Find the sum of odd integers from 1 to 2001.
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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