Q. 294.5( 6 Votes )

Find the sum of all the 3 digit natural numbers which are divisible by 13.

Answer :

The three digit natural numbers which are divisible by 13 are


104, 117, 130,…, 988


a2 – a1 = 117 – 104 = 13


a3 – a2 = 130 – 117 = 13


a3 – a2 = a2 – a1 = 13


Therefore, the series is in AP


Here, a = 104, d = 13 and an = 988


We know that,


an = a + (n – 1)d


988 = 104 + (n – 1)13


988 – 104 = (n – 1)13


884 = (n – 1)13


68 = (n – 1)


n = 69


Now, we have to find the sum of this AP





S69 = 69[104 + 34 × 13]


S69 = 69[546]


S69 = 37674


Hence, the sum of three digit natural numbers which are divisible by 13 are 37674.


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
NCERT | Fundamental Theorem Of Arithmetic45 mins
Quiz on Arithmetic Progression Quiz32 mins
Fundamental Theorem of Arithmetic- 143 mins
Arithmetic progression: Previous Year NTSE Questions34 mins
Get to Know About Geometric Progression41 mins
NCERT | Solving Questions on Introduction of A.P42 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