Q. 44.5( 33 Votes )

The A.P. in which 4th term is – 15 and 9th term is – 30. Find the sum of the first 10 numbers.

Answer :

t4 = – 15 and t9 = – 30

Now, By using nth term of an A.P. formula


tn = a + (n – 1)d


where n = no. of terms


a = first term


d = common difference


tn = nth terms


Hence, by given condition we get,


t4 = – 15


a + (4 – 1)d = – 15


a + 3d = – 15 …..(1)


t9 = – 30


a + (9 – 1)d = – 30


a + 8d = – 30 …..(2)


Subtracting eq. (1) from eq. (2)


[a + 8d] – [a + 3d] = – 30 – ( – 15)


5d = – 30 + 15 = – 15



Substituting, “d” in eq. (1)


a + 3 × ( – 3) = – 15


a + – 9 = – 15


a = – 15 + 9 = – 6


Thus, By using sum of nth term of an A.P. we will find it’s sum



Where, n = no. of terms


a = first term


d = common difference


Sn = sum of n terms


We need to find S10



S10 = 5 [ – 12 + 9 × ( – 3)]


S10 = 5 [ – 12 – 27]


S10 = 5 × ( – 39) = – 195


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
Lets Check Your Knowledge in A.P.Lets Check Your Knowledge in A.P.Lets Check Your Knowledge in A.P.49 mins
Arithmetic progression: Previous Year NTSE QuestionsArithmetic progression: Previous Year NTSE QuestionsArithmetic progression: Previous Year NTSE Questions34 mins
NCERT | Questions on General Term of an A.PNCERT | Questions on General Term of an A.PNCERT | Questions on General Term of an A.P47 mins
Arithmetic Progression Tricks and QUIZArithmetic Progression Tricks and QUIZArithmetic Progression Tricks and QUIZ37 mins
Quiz | Group of Questions on General Term  of an A.PQuiz | Group of Questions on General Term  of an A.PQuiz | Group of Questions on General Term of an A.P49 mins
Master Arithmetic ProgressionMaster Arithmetic ProgressionMaster Arithmetic Progression36 mins
Quiz on  Arithmetic Progression QuizQuiz on  Arithmetic Progression QuizQuiz on Arithmetic Progression Quiz32 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
RELATED QUESTIONS :