Q. 284.5( 6 Votes )

If sum of first 6 terms of an AP is 36 and that of the first 16 terms is 256, then find the sum of first 10 terms.

Answer :

Let a and d be the first term and common difference, respectively of an AP


We know, Sum of first n terms of an AP




36 = 3[ 2a + 5d]


12 = 2a + 5d


2a = 12 - 5d [ eqn 1]


Now,



256 = 8[ 2a + 15d]


32 = 2a + 15d


32 = 12 - 5d + 15d [ using eqn 1]


20 = 10d


d = 2


using this value in eqn 1we get,


2a = 12 - 5(2)


2a = 2


a = 1


Now,



= 5(2 + 9(2))


= 5(20) = 100


So the sum of first 20 terms is 100


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 ProgressionChamp Quiz | Arithmetic ProgressionChamp Quiz | Arithmetic Progression34 mins
Champ Quiz |  Arithmetic ProgressionChamp Quiz |  Arithmetic ProgressionChamp Quiz | Arithmetic Progression30 mins
Quiz | Arithmetic ProgressionQuiz | Arithmetic ProgressionQuiz | Arithmetic Progression44 mins
NCERT | Fundamental Theorem Of ArithmeticNCERT | Fundamental Theorem Of ArithmeticNCERT | Fundamental Theorem Of Arithmetic45 mins
Quiz on  Arithmetic Progression QuizQuiz on  Arithmetic Progression QuizQuiz on Arithmetic Progression Quiz32 mins
NCERT | Arithmetic ProgressionNCERT | Arithmetic ProgressionNCERT | Arithmetic Progression36 mins
Lets Check Your Knowledge in A.P.Lets Check Your Knowledge in A.P.Lets Check Your Knowledge in A.P.49 mins
Get to Know About Geometric ProgressionGet to Know About Geometric ProgressionGet to Know About Geometric Progression41 mins
NCERT | Solving Questions on Introduction of A.PNCERT | Solving Questions on Introduction of A.PNCERT | Solving Questions on Introduction of A.P42 mins
Fundamental Theorem of Arithmetic- 1Fundamental Theorem of Arithmetic- 1Fundamental Theorem of Arithmetic- 143 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