Q. 113.9( 249 Votes )

If the sum of the first n terms of an AP is 4n - n2, what is the first term (that is S1 )?
What is the sum of first two terms? What is the second term? Similarly, find the 3rd, the 10th and the nth terms.

Answer :

As the sum till first term will only contain first term,
   S1 = a1

We can find the first term as follows:
Sn = 4n - n2

So, by putting the values in place of 1 we will get the sum till that term
S1 = 4 × 1 - 12 = 3

Now; sum of first two terms can be calculated as follows:

S2 = 4 × 2 - 22

= 8 - 4 = 4

Hence, S2 = 4
Now we know by the formula that: Sn - Sn - 1 = an

Hence; second term = 4 – 3 = 1

And second term - first term = common difference of AP

Therefore, common difference,  d = 1 – 3 = - 2

Now we have the AP as follows
First term, a = 3
Common difference = -2
So AP will look like : 3, 1, -1, -3, -5, ..........................
And, nth term of an AP is given by the formula,
 
an = a + (n - 1)d
Putting the value of a and d in above formula we get
an = 3 + (n - 1) -2
an = 3 - 2n + 2
an = 5 - 2n

So, 3rd term can be can be calculated by just replacing n with 3
a3 = 5 - 2 x 3
a3 = -1
Similarly
a10 = 5 - 2x 10
a10 = -15
 
And so on we can calculate any number of terms of this AP

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
Smart Revision | Arithmetic ProgressionSmart Revision | Arithmetic ProgressionSmart Revision | Arithmetic Progression47 mins
Champ Quiz |  Arithmetic ProgressionChamp Quiz |  Arithmetic ProgressionChamp Quiz | Arithmetic Progression30 mins
Quiz | Arithmetic ProgressionQuiz | Arithmetic ProgressionQuiz | Arithmetic Progression44 mins
Smart Revision | General Term of an A.PSmart Revision | General Term of an A.PSmart Revision | General Term of an A.P44 mins
NCERT | Fundamental Theorem Of ArithmeticNCERT | Fundamental Theorem Of ArithmeticNCERT | Fundamental Theorem Of Arithmetic45 mins
Lets Check Your Knowledge in A.P.Lets Check Your Knowledge in A.P.Lets Check Your Knowledge in A.P.49 mins
Quiz on  Arithmetic Progression QuizQuiz on  Arithmetic Progression QuizQuiz on Arithmetic Progression Quiz32 mins
NCERT | Arithmetic ProgressionNCERT | Arithmetic ProgressionNCERT | Arithmetic Progression36 mins
Get to Know About Geometric ProgressionGet to Know About Geometric ProgressionGet to Know About Geometric Progression41 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