##### VMC VIQ Scholarship Test

ApplyRegister for Vidyamandir Intellect Quest. Get Scholarship and Cash Rewards.

Edited By Ravindra Pindel | Updated on Sep 12, 2022 04:04 PM IST

**NCERT Exemplar Class 11 Maths Solutions Chapter 9** has been assembled very carefully by our experts. These solutions make students aware of various concepts and methods associated with sequence and series through the easiest ways accepted by CBSE. A sequence in Mathematics has the same sense as it is in English, which denotes the arrangement of numbers in some specific order so that every number could be identified independently. NCERT Exemplar Class 11 Maths chapter 9 solutions cover a variety of topics linked with sequence and series. Class 11 Maths NCERT exemplar solutions chapter 9 also help with establishing relationships between different terms of sequence and series followed by varied numerical problems and their solutions for practice and a better understanding of the concept.**Also, check -** NCERT Class 11 Solutions Maths for other chapters.

**JEE Main Scholarship Test Kit (Class 11): Narayana | Physics Wallah | **

**Suggested: ****JEE Main: high scoring chapters | ****Past 10 year's papers**

**Scholarship Test:** **Vidyamandir Intellect Quest (VIQ)**

Question:1

Answer:

The sum of first p terms and the first term is given. We have to find next q terms. So, the total terms become p+q.

Hence, sum of all terms minus the sum of first p terms will give the sum of next q terms. However, sum of first p terms is zero, so the sum of next q terms will be same as sum of all terms.

Sum of n terms is given by

Replacing the value of d in equation (i)

Question:2

Answer:

Total amount saved in 20 years is

Let the amount saved in first year be ‘a’

Since he increases 200 Rs every year, d=200

Sum formula of A.P is

Question:3

Answer:

The man’s salary in first month is Rs. 5200 and increases every month by Rs. 320. So, we have the value of ‘a’ and ‘d’.

Salary in 10^{th} month is given by

For total earnings in first year, the first 12 terms of the sequence are added.

Question:4

If the terms of a G.P. are q and p respectively, show that its term is

Answer:

The nth term is given by

The pth term is given by

Question:5

Answer:

The first day he made 5 frames and 2 more frames each passing day. So,

a=5 and d=2

Let us assume that it takes ‘n’ days to build 192 window frames

Since number of days can’t be negative n=12

Question:6

Answer:

The sum of interir angles of a polygon having 'n' sides is given by

By this formula sum of angles with 3 sides, 4 sides, 5 sides and 6 sides is

respectively. As the number of side increases by 1, the sum of interior angle increases by

So,for sum of angles of polygon with 21 sides

Question:7

Answer:

Let AB=BC=AC=20cm

Let D, E and F be midpoints of AC, CB and AB which are joined to form an equilateral triangle DEF. So, CD=CE=10cm. Triangle CDE is equilateral. Hence, DE= 10 cm. Similarly, GH = 5 cm

The series of sides of equilateral triangle will be 20,10,5…..

The series is a G.P with first term 20 and common ratio =1/2

For the perimeter of 6^{th} triangle we first have to find the side of 6^{th} triangle

Perimeter would be thrice the length of its side.

Perimeter of triangle=

Question:8

Answer:

It is given that at start he has to run 24m to get the first potato then 28 m as the next potato is 4m away and so on.

Hence, the sequence of its running will be 24, 28, 32…..

To get potatoes from the starting point he has to run 24+ 28+ 32+….. up to 20 terms

Also, he has to get the potato back to the starting point hence the total distance will be twice

Total Distance ran=2×1240=2480m

Question:9

Answer:

Let the amount received by first place be Rs. A and ‘d’ be the difference in the amount. The last team receives Rs. 275. As there are 16 teams and all teams are given prizes hence the sequence will have 16 terms because there are 16 teams.

As total prize given is of 8000 rs hence

Question:11

Find the sum of the series to (i) n terms

(ii) 10 terms

Answer:

Generalising the series in terms of i

Sum up to n terms

Question:12

Find the rth term of an A.P. sum of whose first n terms is .

Answer:

Sum of first n terms is given by

The rth term is

Question:13

If A is the arithmetic mean and , be two geometric means between any two numbers, then prove that

Answer:

It is given that A is the arithmetic mean and , be two geometric means between any two numbers.

Question:15

Answer:

The sum of n terms is given by

Where ‘a’ is the first term and ’d’ is the common difference

Question:16

If , , and terms of an A.P. and G.P. are both a, b and c respectively, show that

Answer:

Let the first term of AP be m and common difference as d. Let the first term of GP be I and common ratio be s.

For AP

For GP

Question:17

If the sum of n terms of an A.P. is given by , then the common difference of the A.P. is

(A) 3 (B) 2 (C) 6 (D) 4

Answer:

Given that

We know that

Hence, correct option is d.

Question:18

The third term of G.P. is 4. The product of its first 5 terms is

(A) 4^{3} (B) 4^{4} (C) 4^{5} (D) None of these

Answer:

The third term of G.P is given

Product of first 5 terms

Hence, correct option is c.

Question:19

If 9 times the 9th term of an A.P. is equal to 13 times the 13th term, then the 22nd term of the A.P. is

A. 0

B. 22

C. 220

D. 198

Answer:

Hence, correct option is a.

Question:20

If x, 2y, 3z are in A.P., where the distinct numbers x, y, z are in G.P. then the common ratio of the G.P. is

A. 3

B. 1/3

C. 2

D. 1/2

Answer:

It is given that x, 2y and 3z are in A.P

Hence, correct option is b.

Question:21

If in an A.P., Sn = qn^{2} and Sm = qm^{2}, where S_{r} denotes the sum of r terms of the A.P., then S_{q} equals

A.

B. mnq

C.

D.

Answer:

The given series is an A.P with first term ‘a’ and common difference ‘d’.

Hence, correct option is c.

Question:22

Let denote the sum of the first n terms of an A.P. If then is equal to

A. 4

B. 6

C. 8

D. 10

Answer:

Given

Hence, the correct option is b.

Question:23

The minimum value of is

A. 2

B. 4

C. 1

D. 0

Answer:

The AM-GM inequality states that the arithmetic mean of a list of non-negative real numbers is greater than or equal to the geometric mean of the same list

Hence, correct option is b.

Question:24

Let denote the sum of the cubes of the first n natural numbers and denote the sum of the first n natural numbers. Then equals.

A.

B.

C.

D. None of these

Answer:

Sum of cubes of first n natural numbers

Sum of first n natural numbers

Hence, correct option is (a).

Question:25

If denotes the term of the series then is

A.

B.

C.

D.

Answer:

(Using method of difference)

Hence, correct option is d.

Question:26

The lengths of three unequal edges of a rectangular solid block are in G.P. The volume of the block is and the total surface area is . The length of the longest edge is

A. 12 cm

B. 6 cm

C. 18 cm

D. 3 cm

Answer:

The volume and total S.A of a block are given

Let the length, breadth and height of a rectangular block be given by respectively.

If a = 6 and r=2 then l,b and h are respectively.

If a=6 and r=1/2 then l,b and h are 12, 6 and 3 respectively.

In both the cases, the longest side is 12 units.

Hence, correct option is a.

Question:27

Fill in the blanks

For a, b, c to be in G.P. the value of is equal to ..........

Answer:

It is given that a, b, c are in G.P

Question:28

Answer:

Taking first and last terms of

Taking k-th and (n-k+1) -th term

Question:29

Answer:

The third term of a G.P is given by

Let the common ratio be ‘r’

Product of first 5 terms

Question:30

State whether statement in True or False. Two sequences cannot be in both A.P. and G.P. together.

Answer:

Let the terms of A.P be

Let the terms of G.P be

So the terms of A.P and G.P are same

Question:31

Answer:

A progression is a sequence, but a sequence is not a progression because it does not follow a specific pattern.

Hence, the given statement is TRUE.

Question:32

Answer:

Let us consider an A.P a, a+d, a+2d, a+3d

Hence, the given statement is TRUE.

Question:33

State whether statement in True or False. The sum or difference of two G.P.s, is again a G.P.

Answer:

Let the two G.P be

And

The terms of sum of these two G.P are

The terms of difference of two G.P are

Hence, the difference and sum of 2 G.P is not a G.P because common ratio is not same.

Question:34

Answer:

For n=1

So, it does not represent an AP because common difference is not same.

Question:35

Match the questions given under Column I with their appropriate answers given under the Column II.

Column-I | Column-II |

a) | i) A.P. |

b) | ii) Sequence |

c) | iii)G.P. |

Answer:

Hence, the given numbers is in G.P with common ratio

Hence, it is not in AP

Now, we will check the ratio

Question:36

Match the questions given under Column I with their appropriate answers given under the Column II.

Column-I | Column-II |

a) | i) |

b) | ii) |

c) | iii) |

d) | iv) |

Answer:

Sum of ‘n’ natural numbers

Sum of cube of ‘n’ natural numbers

Sum of square of ‘n’ natural numbers

Sum of twice times ‘n’ natural numbers

So, (a) – (iii), (b)- (i), (c)- (ii), (d)- (iv)

The students can access NCERT Exemplar Class 11 Maths solutions chapter 9 PDF download for better understanding and learning experience through precisely drafted solutions by our experts.

The NCERT Exemplar solutions for Class 11 Maths chapter 9 provided here are very precise yet simple for better understanding and help of students for practice and preparation of their exams.

- 9.1 Introduction
- 9.2 Sequences
- 9.3 Series
- 9.4 Arithmetic Progression (A.P.)
- 9.4.1 Arithmetic mean (A.P.)
- 9.5 Geometric Progression (G.P.)
- 9.5.1 General term of a G.P.
- 9.5.2 Sum of n terms of a G.P.
- 9.5.3 Geometric mean (G.M.)
- 9.6 Relationship Between A.M. and G.M.
- 9.7 Sum of n terms of Special series
- 9.8 Miscellaneous examples

The students will learn different concepts of sequence and series that will help them in other mathematical disciplines such as differential equations and their analysis.

NCERT Exemplar Class 11 Maths solutions Chapter 9 also helps in developing the analytical thinking, critical thinking and reasoning of the learners, which is helpful in competitive exams along with real-life situations.

The concept of sequence and series are also helpful in various different subjects for higher education, along with its use in subjects like physics.

The concept also gives an insight into its application in various different fields like astronomy, physics, chemistry, biology, finance, architecture, medicine and much more in every other aspect of science and mathematics.

**NCERT Exemplar Class 11 Maths Solutions Chapter-Wise**

Some of the important topics for students to review are as follows:

· The students should learn about different sequences, including arithmetic and geometric progressions, its properties along with its importance in mathematics.

· NCERT Exemplar Class 11 Maths chapter 9 solutions cover the sum of elements of any sequence referred to as series whether finite or infinite and its representation through the compact form of sigma notation.

· NCERT Exemplar Class 11 Maths solutions chapter 9 also includes the study of arithmetic and the geometric mean of sequences.

· The students must practice the numerical and solutions of this chapter from the exam point of view.

· NCERT Exemplar solutions for Class 11 Maths chapter 9 also derives the relation between the arithmetic mean and the geometric mean of any sequence and its formulas.

**Check Chapter-Wise NCERT Solutions of Book**

Chapter-1 | |

Chapter-2 | |

Chapter-3 | |

Chapter-4 | |

Chapter-5 | |

Chapter-6 | |

Chapter-7 | |

Chapter-8 | |

Chapter-9 | |

Chapter-10 | |

Chapter-11 | |

Chapter-12 | |

Chapter-13 | |

Chapter-14 | |

Chapter-15 | |

Chapter-16 |

**Read more NCERT Solution subject wise -**

- NCERT Solutions for Class 11 Maths
- NCERT Solutions for Class 11 Physics
- NCERT Solutions for Class 11 Chemistry
- NCERT Solutions for Class 11 Biology

JEE Main Highest Scoring Chapters & Topics

Just Study 40% Syllabus and Score upto 100%

Download EBook**Also, read NCERT Notes subject wise -**

- NCERT Notes for Class 11 Maths
- NCERT Notes for Class 11 Physics
- NCERT Notes for Class 11 Chemistry
- NCERT Notes for Class 11 Biology

**Also Check NCERT Books and NCERT Syllabus here:**

1. What are some of the important topics of this chapter?

Some of the important topics of NCERT Exemplar Class 11 Maths Chapter 9 Sequence and Series are arithmetic progression, arithmetic mean, geometric progression, geometric mean, and the relationship between geometric mean and arithmetic mean.

2. Are these solutions useful from an exam point of view?

Yes, NCERT exemplar Class 11 Maths solutions chapter 9 are very important for any type of exam as they provide a better understanding and explanation of different types of concept through easier methods.

3. Where can I download the solutions for this chapter?

NCERT Exemplar solutions for Class 11 Maths Chapter 9 can be easily downloaded in PDF format by using the webpage pdf download online tools.

Application Date:05 September,2024 - 20 September,2024

Admit Card Date:13 September,2024 - 07 October,2024

Admit Card Date:13 September,2024 - 07 October,2024

Application Date:17 September,2024 - 30 September,2024

Get answers from students and experts

Register for Vidyamandir Intellect Quest. Get Scholarship and Cash Rewards.

Register for Tallentex '25 - One of The Biggest Talent Encouragement Exam

As per latest 2024 syllabus. Physics formulas, equations, & laws of class 11 & 12th chapters

As per latest 2024 syllabus. Chemistry formulas, equations, & laws of class 11 & 12th chapters

Accepted by more than 11,000 universities in over 150 countries worldwide

Register now for PTE & Unlock 10% OFF : Use promo code: 'C360SPL10'. Limited Period Offer! Trusted by 3,500+ universities globally

News and Notifications

Back to top