Q. 275.0( 2 Votes )

Find the sum of all the three digit natural numbers which are multiples of 7.

Answer :

The three digit natural numbers which are multiples of 7 are


105, 112, 119,…, 994


a2 – a1 = 112 – 105 = 7


a3 – a2 = 112 – 105 = 7


a3 – a2 = a2 – a1 = 7


Therefore, the series is in AP


Here, a = 105, d = 7 and an = 994


We know that,


an = a + (n – 1)d


994 = 105 + (n – 1)7


994 – 105 = (n – 1)7


889 = (n – 1)7


127 = (n – 1)


n = 128


Now, we have to find the sum of this AP




S128 = 64[210 + 127 × 7]


S128 = 64[1099]


S128 = 70336


Hence, the sum of all three digit numbers which are multiples of 7 are 70336.


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