Q. 1 D5.0( 1 Vote )

Find the sum of the following series.

7 + 14 + 21…. + 490

Answer :

Given the series S = 7 + 14 + 21…. + 490,


We see that there is a common term 7 in all the numbers in the series. Taking 7 common, we have


S = 7(1 + 2 + 3 + .. + 70)


Let 1 + 2 + 3 + .. + 70 be S1, with n = 70


So S becomes S = 7S1


To find S1-


Formula for sum of first n numbers is


S1 =




35 × 71


= 2485


S = 7S1


S = 7 × 2485 = 17395


The sum S = 7 + 14 + 21…. + 490 = 17395


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:Euclid's Division LemmaInteractive Quiz:Euclid's Division LemmaInteractive Quiz:Euclid's Division Lemma44 mins
Fundamental Theorem of Arithmetic-2Fundamental Theorem of Arithmetic-2Fundamental Theorem of Arithmetic-238 mins
Champ Quiz | Fundamental Principle Of ArithmeticChamp Quiz | Fundamental Principle Of ArithmeticChamp Quiz | Fundamental Principle Of Arithmetic41 mins
Euclids Division LemmaEuclids Division LemmaEuclids Division Lemma49 mins
Fundamental Theorem of Arithmetic- 1Fundamental Theorem of Arithmetic- 1Fundamental Theorem of Arithmetic- 143 mins
Quiz | Imp Qs on Real NumbersQuiz | Imp Qs on Real NumbersQuiz | Imp Qs on Real Numbers37 mins
NCERT | Imp. Qs. on Rational and Irrational NumbersNCERT | Imp. Qs. on Rational and Irrational NumbersNCERT | Imp. Qs. on Rational and Irrational Numbers44 mins
Application of Euclids Division LemmaApplication of Euclids Division LemmaApplication of Euclids Division Lemma50 mins
Relation Between LCM , HCF and NumbersRelation Between LCM , HCF and NumbersRelation Between LCM , HCF and Numbers46 mins
Quiz | Fun with Fundamental Theorem of ArithmeticQuiz | Fun with Fundamental Theorem of ArithmeticQuiz | Fun with Fundamental Theorem of Arithmetic51 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
caricature
view all courses