Q. 20 A5.0( 2 Votes )

Find the sum of all the odd numbers lying between 100 and 200.

Answer :

The odd numbers lying between 100 and 200 are


101, 103, 105,…, 199


a2 – a1 = 103 – 101 = 2


a3 – a2 = 105 – 103 = 2


a3 – a2 = a2 – a1 = 2


Therefore, the series is in AP


Here, a = 101, d = 2 and an = 199


We know that,


an = a + (n – 1)d


199 = 101 + (n – 1)2


199 – 101 = (n – 1)2


98 = (n – 1)2


49 = (n – 1)


n = 50


Now, we have to find the sum of this AP




S50 = 25[202 + 49 × 2]


S50 = 25[300]


S50 = 7500


Hence, the sum of all odd numbers lying between 100 and 200 is 7500.


Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
Related Videos
Champ Quiz | Arithmetic Progression34 mins
Champ Quiz | Arithmetic Progression30 mins
Lets Check Your Knowledge in A.P.49 mins
Fundamental Theorem of Arithmetic- 143 mins
Quiz on Arithmetic Progression Quiz32 mins
NCERT | Fundamental Theorem Of Arithmetic45 mins
Get to Know About Geometric Progression41 mins
NCERT | Solving Questions on Introduction of A.P42 mins
Arithmetic progression: Previous Year NTSE Questions34 mins
Arithmetic Progression Tricks and QUIZ37 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