Q. 84.3( 232 Votes )

An AP consists of 50 terms of which 3rd term is 12 and the last term is 106. Find the 29thterm.

Answer :

Given, a3 = 12 and a50 = 106

We know that nth term of an AP is given by
an = a + (n - 1)d
where, an = nth term of the AP
a = first term of AP
n = number of terms of AP
d = common difference of AP
Applying the formula for 3rd and 50th term we get,

a3 = a + 2d = 12

a50 = a + 49d = 106


Subtracting 3rd term from 50th term, we get;


a + 49d – a – 2d = 106 – 12


47d = 94


d = 2


Substituting the value of d in 3rd term, we get;


a + 2 x 2 = 12


Or, a + 4 = 12


Or, a = 8


Now, 29th term can be calculated as follows:


a29 = a + 28d


= 8 + 28 x 2


= 8 + 56 = 64

a29 = 64

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
Smart Revision | Arithmetic ProgressionSmart Revision | Arithmetic ProgressionSmart Revision | Arithmetic Progression47 mins
NCERT | Fundamental Theorem Of ArithmeticNCERT | Fundamental Theorem Of ArithmeticNCERT | Fundamental Theorem Of Arithmetic45 mins
Fundamental Theorem of Arithmetic- 1Fundamental Theorem of Arithmetic- 1Fundamental Theorem of Arithmetic- 143 mins
Quiz on  Arithmetic Progression QuizQuiz on  Arithmetic Progression QuizQuiz on Arithmetic Progression Quiz32 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
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