Find the best tutors and institutes for Class 11 Tuition
Sequences and Series EXERCISE 8.2 Solutions
- Q1: Find the 20th and nth terms of the G.P. $\frac{5}{2}, \frac{5}{4}, \frac{5}{8}, ...$
- Q2: Find the 12th term of a G.P. whose 8th term is 192 and the common ratio is 2.
- Q3: The 5th, 8th and 11th terms of a G.P. are $p, q$ and $s$, respectively. Show that $q^2 = ps$.
- Q4: The 4th term of a G.P. is square of its second term, and the first term is -3. Determine its 7th term.
- Q5(a): Which term of the following sequence: (a) $2, 2\sqrt{2}, 4, ...$ is 128?
- Q5(b): Which term of the following sequence: (b) $\sqrt{3}, 3, 3\sqrt{3}, ...$ is 729?
- Q5(c): Which term of the following sequence: (c) $\frac{1}{3}, \frac{1}{9}, \frac{1}{27}, ...$ is $\frac{1}{19683}$?
- Q6: For what values of $x$, the numbers $-\frac{2}{7}, x, -\frac{7}{2}$ are in G.P.?
- Q7: Find the sum to indicated number of terms in the geometric progression: 0.15, 0.015, 0.0015, ... 20 terms.
- Q8: Find the sum to indicated number of terms in the geometric progression: $\sqrt{7}, \sqrt{21}, 3\sqrt{7}, ...$ $n$ terms.
- Q9: Find the sum to indicated number of terms in the geometric progression: $1, -a, a^2, -a^3, ...$ $n$ terms (if $a \ne -1$).
- Q10: Find the sum to indicated number of terms in the geometric progression: $x^3, x^5, x^7, ...$ $n$ terms (if $x \ne \pm 1$).
- Q11: Evaluate $\sum_{k=1}^{11} (2 + 3^k)$.
- Q12: The sum of first three terms of a G.P. is $\frac{39}{10}$ and their product is 1. Find the common ratio and the terms.
- Q13: How many terms of G.P. $3, 3^2, 3^3, ...$ are needed to give the sum 120?
- Q14: The sum of first three terms of a G.P. is 16 and the sum of the next three terms is 128. Determine the first term, the common ratio and the sum to $n$ terms of the G.P.
- Q15: Given a G.P. with $a = 729$ and 7th term 64, determine $S_7$.
- Q16: Find a G.P. for which sum of the first two terms is -4 and the fifth term is 4 times the third term.
- Q17: If the 4th, 10th and 16th terms of a G.P. are $x, y$ and $z$, respectively. Prove that $x, y, z$ are in G.P.
- Q18: Find the sum to $n$ terms of the sequence, 8, 88, 888, 8888... .
- Q19: Find the sum of the products of the corresponding terms of the sequences 2, 4, 8, 16, 32 and 128, 32, 8, 2, $\frac{1}{2}$.
- Q20: Show that the products of the corresponding terms of the sequences $a, ar, ar^2, ...ar^{n-1}$ and $A, AR, AR^2, ... AR^{n-1}$ form a G.P, and find the common ratio.
- Q21: Find four numbers forming a geometric progression in which the third term is greater than the first term by 9, and the second term is greater than the 4th by 18.
- Q22: If the $p^{th}, q^{th}$ and $r^{th}$ terms of a G.P. are $a, b$ and $c$, respectively. Prove that $a^{q-r} b^{r-p} c^{p-q} = 1$.
- Q23: If the first and the $n^{th}$ term of a G.P. are $a$ and $b$, respectively, and if $P$ is the product of $n$ terms, prove that $P^2 = (ab)^n$.
- Q24: Show that the ratio of the sum of first $n$ terms of a G.P. to the sum of terms from $(n + 1)^{th}$ to $(2n)^{th}$ term is $\frac{1}{r^n}$.
- Q25: If $a, b, c$ and $d$ are in G.P. show that $(a^2 + b^2 + c^2) (b^2 + c^2 + d^2) = (ab + bc + cd)^2$.
- Q26: Insert two numbers between 3 and 81 so that the resulting sequence is G.P.
- Q27: Find the value of $n$ so that $\frac{a^{n+1} + b^{n+1}}{a^n + b^n}$ may be the geometric mean between $a$ and $b$.
- Q28: The sum of two numbers is 6 times their geometric mean, show that numbers are in the ratio $(3 + 2\sqrt{2}) : (3 - 2\sqrt{2})$.
- Q29: If A and G be A.M. and G.M., respectively between two positive numbers, prove that the numbers are $A \pm \sqrt{(A+G)(A-G)}$.
- Q30: The number of bacteria in a certain culture doubles every hour. If there were 30 bacteria present in the culture originally, how many bacteria will be present at the end of 2nd hour, 4th hour and $n^{th}$ hour?
- Q31: What will Rs 500 amounts to in 10 years after its deposit in a bank which pays annual interest rate of 10% compounded annually?
- Q32: If A.M. and G.M. of roots of a quadratic equation are 8 and 5, respectively, then obtain the quadratic equation.
Other Exercises for CBSE - Class 11 Mathematics Sequences and Series
Chapters in CBSE - Class 11 Mathematics
Top Tutors who teach Sequences and Series
Top Tutor 
HSR Layout, Bangalore 
7 yrs of Exp 
500 per hour 
Online Classes 
Tutor's home I begin by laying a strong foundation in the core concepts, as Class 11 Mathematics can be complex. Topics like Sets, Relations and Functions, Trigonometry, Polynomials, Calculus, and Statistics are carefully introduced, with a focus on understanding the fundamental principles behind each concept. I focus on explaining problem-solving strategies. For example, in topics like Integration and Differentiation, I guide the student through the basic rules and formulas and then demonstrate their applications step-by-step. I provide practice problems that increase in difficulty to help students master each topic. Mathematics requires a lot of practice, so I assign students a range of problems from basic to advanced, ensuring they have exposure to all types of questions. For example, in Trigonometry, I ensure that students are comfortable with various identities, equations, and properties before moving on to solving higher-level problems. Before exams, I provide focused revision sessions where I go through previous year’s questions, helping students learn how to structure their answers and manage time effectively during exams.
Top Tutor Powai, Mumbai 5 yrs of Exp 
5 students 
124 hrs of classes completed 500 per hour Online Classes Tutor's home I have been teaching Physics to students of Class 11 and 12 for the past five years. During this time, I have guided students through board exams as well as competitive exams like IIT-JEE, helping them strengthen their understanding of concepts, develop problem-solving skills, and improve their overall academic performance. Watching students succeed and gain confidence in Physics has been incredibly rewarding. I am currently pursuing my M.Sc. in Physics, which allows me to stay updated with advanced concepts and recent developments in the field. This academic background enables me to teach complex topics in a structured and understandable way, making them accessible to students at different levels. Over the past five years, I have worked with a diverse group of students, including those preparing for highly competitive exams. This experience has helped me develop effective teaching strategies, advanced problem-solving techniques, and exam-oriented approaches that prepare students for both boards and competitive assessments. My classes are designed to be interactive and engaging. I follow a structured lesson plan that ensures systematic coverage of topics while encouraging active student participation. I use PPTs and the whiteboard to simplify difficult concepts and make learning more visual and practical. I conduct both online and offline sessions, offering flexibility to students while maintaining a high level of interaction. Whether in-person or virtual, I ensure that students receive personalized attention, have their doubts clarified promptly, and develop a strong understanding of each topic. Regular assessments, practice sessions, and feedback are an integral part of my teaching approach. By tracking each student’s progress, I can identify areas that need reinforcement and provide targeted guidance to help them improve steadily and achieve consistent results. My goal as a Physics teacher is to make the subject both approachable and enjoyable. I strive to instill curiosity, analytical thinking, and confidence in students, helping them not only excel academically but also develop problem-solving skills that will benefit them throughout their educational journey.
Sir, helped prepare me for my physics exam and made sure I prepare well by giving extra time and efforts.
Top Tutor Ekta Nagar, Ferozepur 20 yrs of Exp 1 student 8 hrs of classes completed 400 per hour Online Classes Tutor's home I am a Mathematics Teacher with 20 years of teaching experience currently teaching at Paradise School, Zira. I speak English, Hindi and Punjabi. I teach classes 10-12 and I am able to provide both group sessions and online one to one classes. I am qualified in M.Sc of Mathematics, B.Ed, MCA.
Sir was very helpful throughout my class, he teaches very good and explains every question again and again if we don't understand. Overall it was very good.
Super Tutor Nerul, Mumbai 10 yrs of Exp 6 students 542 hrs of classes completed 800 per hour Online Classes I'm an ex-faculty member of Allen, FIITJEE & Unacademy, and I taught in DAV for 2 years. Now I'm working as a freelancer. I have more than 10 years of experience. So overall I've all kinds of experience to meet with academic & JEE aspirants as well. Join me to learn mathematics from basic to advanced.
Sir, explains topics very clearly nicely explains doubt very nicely with high conceptual knowledge.
Super Tutor Bellandur, Bangalore 20 yrs of Exp 6 students 1768 hrs of classes completed 750 per hour Online Classes I am a Chartered Accountant with M. Com, M.Phil, IFRS, Diploma in Banking & Finance and served as Professor of commerce. I am also tutoring accountancy students across various levels. I am focusing on early buds (grades XI and XII) in tutoring to strengthen the fundamentals of accounting and conceptual clarity to buddy accountancy students. This is just to lay a strong foundation to a great super structure in their accounting career. To change the way of traditional teaching, introduced thought provoking discussion on each and every concept or sub-lession that make students to learn by seeking knowledge with smart questioning skills. Periodical assessments are conducted and reviews are shared with students and parents to progress as intended and motivate the students in the challenging areas of learning. Academic counselling is provided to students and parents to choose the best career path after reasonable assessment of students' skill set and interests. Overall, I am very focused to build a strong accounting career for buddy accounting students.
