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.

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Interactive quiz on inequalities involving AM and GM45 mins
Check Your progress Part 2| Interactive Quiz: Sequence & Series47 mins
Sequence & Series (Lecture 1)56 mins
Sequence & Series (Lecture 5)42 mins
Sequence & Series (Lecture 7)37 mins
Use of sigma in finding sum42 mins
Trigonometric Series45 mins
Quick Recap lecture of Sequence & Series56 mins
General Term of Miscellaneous progression46 mins
Improve your understanding of AP & GP27 mins
Try our Mini CourseMaster Important Topics in 7 DaysLearn from IITians, NITians, Doctors & Academic Experts
Dedicated counsellor for each student
24X7 Doubt Resolution
Daily Report Card
Detailed Performance Evaluation
view all courses