Which term of the following sequences: | Class 11 Mathematics Chapter Sequence and Series, Sequence and Series NCERT Solutions

Welcome to the NCERT Solutions for Class 11 Mathematics - Chapter Sequence and Series. This page offers a step-by-step solution to the specific question from Exercise 3, Question 5: . With detailed answers and explanations for each chapter, students can strengthen their understanding and prepare confidently for exams. Ideal for CBSE and other board students, this resource will simplify your study experience.

Question 5:

Which term of the following sequences:

$2 comma space 2 square root of 2 comma 4 comma space...$

Answer:

(a) The given sequence is $2 comma space 2 square root of 2 comma 4 comma space...$

Here, a = 2 and r = $fraction numerator 2 square root of 2 over denominator 2 end fraction equals square root of 2$

Let the nth term of the given sequence be 128.

$a subscript n space end subscript equals space a r to the power of n minus 1 end exponent rightwards double arrow open parentheses 2 close parentheses open parentheses square root of 2 close parentheses to the power of n minus 1 end exponent space equals space 128 rightwards double arrow open parentheses 2 close parentheses open parentheses 2 close parentheses to the power of fraction numerator n minus 1 over denominator 2 end fraction end exponent equals open parentheses 2 close parentheses to the power of 7 rightwards double arrow open parentheses 2 close parentheses to the power of fraction numerator n minus 1 over denominator 2 end fraction plus 1 end exponent equals open parentheses 2 close parentheses to the power of 7 s o space fraction numerator n minus 1 over denominator 2 end fraction plus 1 equals 7 rightwards double arrow fraction numerator n minus 1 over denominator 2 end fraction space equals space 6 rightwards double arrow n space minus 1 space equals space 12 rightwards double arrow n equals 13$

Thus, the 13th term of the given sequence is 128.

(b) The given sequence is $square root of 3 space comma space 3 comma space 3 square root of 3 space comma space... space i s space 729 ?$

Here, a= $square root of 3 space a n d space r space equals space fraction numerator 3 over denominator square root of 3 end fraction space equals space square root of 3$

Let the nth term of the given sequence be 729.

$a subscript n equals a r to the power of n minus 1 end exponent s o a r to the power of n minus 1 end exponent space equals space 729 rightwards double arrow open parentheses square root of 3 close parentheses space open parentheses square root of 3 close parentheses to the power of n minus 1 end exponent space equals space 729 rightwards double arrow open parentheses 3 close parentheses to the power of 1 half end exponent open parentheses 3 close parentheses to the power of fraction numerator n minus 1 over denominator 2 end fraction end exponent equals open parentheses 3 close parentheses to the power of 6 rightwards double arrow open parentheses 3 close parentheses to the power of 1 half plus fraction numerator n minus 1 over denominator 2 end fraction end exponent equals open parentheses 3 close parentheses to the power of 6 s o 1 half plus fraction numerator n minus 1 over denominator 2 end fraction equals 6 rightwards double arrow fraction numerator 1 plus n minus 1 over denominator 2 end fraction equals 6 rightwards double arrow n equals 12$

Thus, the 12th term of the given sequence is 729.

(c) The given sequence is $1 third comma space 1 over 9 comma space 1 over 27 comma space... space$

Here,

a= $1 third space space a n d space r space equals space 1 over 9 obelus divided by 1 third equals 1 third$

Let the nth term of the given sequence be $1 over 19683$ .

$a subscript n space equals space a r to the power of n minus 1 end exponent s o a r to the power of n minus 1 end exponent equals 1 over 19683 rightwards double arrow open parentheses 1 third close parentheses open parentheses 1 third close parentheses to the power of n minus 1 end exponent equals 1 over 19683 rightwards double arrow open parentheses 1 third close parentheses to the power of n equals open parentheses 1 third close parentheses to the power of 9 rightwards double arrow n equals 9$

Thus, the 9th term of the given sequence is $1 over 19683$ .

Other Questions of Chapter Sequence and Series

How many terms of G.P. 3, 3², 3³, … are needed to give the sum 120?

Find the sum to n terms of the series whose nth terms is given by (2n – 1)²

The sum of the first four terms of an A.P. is 56. The sum of the last four terms is 112. If its first term is 11, then find the number of terms.

If the sum of three numbers in A.P., is 24 and their product is 440, find the numbers.

Find a G.P. for which sum of the first two terms is –4 and the fifth term is 4 times the third term.

Find the 12th term of a G.P. whose 8th term is 192 and the common ratio is 2.

Let the sum of n, 2n, 3n terms of an A.P. be S₁, S₂ and S₃, respectively, show that S₃ = 3 (S₂– S₁)

If the p^th, q^th and r^th terms of a G.P. are a, b and c, respectively. Prove that a^q-rb^r-pc^p-q=1

Find the sum to 20 terms in the geometric progression 0.15, 0.015, 0.0015 …

Q: Write the first five terms of the sequences whose nth term is a_n=n(n+2)

Popular questions of class 11 Mathematics

A wheel makes 360 revolutions in one minute. Through how many radians does it turn in one second?

Q: Write the following sets in roster form:
(i) A = {x: x is an integer and - 3 < x < 7}.
(ii) B = {x: x is a natural number less than 6}.
(iii) C = {x: x is a two-digit natural number such that the sum of its digits is 8}
(iv) D = {x: x is a prime number which is divisor of 60}.
(v) E = The set of all letters in the word TRIGONOMETRY.
(vi) F = The set of all letters in the word BETTER.

Q: Write the following sets in the set-builder form:
(i) (3, 6, 9, 12)
(ii) {2, 4, 8, 16, 32}
(iii) {5, 25, 125, 625}
(iv) {2, 4, 6 upto infinity}
(v) {1, 4, 9, upto 100}

How many 4-letter code can be formed using the first 10 letters of the English alphabet, if no letter can be repeated?

Name the octants in which the following points lie:

(1, 2, 3), (4, –2, 3), (4, –2, –5), (4, 2, –5), (–4, 2, –5), (–4, 2, 5), (–3, –1, 6), (2, –4, –7)

A point is in the XZ-plane. What can you say about its y-coordinate?

How many 3-digit numbers can be formed from the digits 1, 2, 3, 4 and 5 assuming that

(i) repetition of the digits is allowed?

(ii) repetition of the digits is not allowed?

Which of the following sentences are statements? Give reasons for your answer.

(i) There are 35 days in a month.

(ii) Mathematics is difficult.

(iii) The sum of 5 and 7 is greater than 10.

(iv) The square of a number is an even number.

(v) The sides of a quadrilateral have equal length.

(vi) Answer this question.

(vii) The product of (–1) and 8 is 8.

(viii) The sum of all interior angles of a triangle is 180°.

(ix) Today is a windy day.

(x) All real numbers are complex numbers.

An experiment consists of tossing a coin and then throwing it second time if a head occurs. If a tail occurs on the first toss, then a die is rolled once. Find the sample space.

A coin is tossed 3 times and the outcomes are recorded. How many possible outcomes are there?

Recently Viewed Questions of Class 11 Mathematics

The base of an equilateral triangle with side 2a lies along the y-axis such that the mid-point of the base is at the origin. Find vertices of the triangle.

A point is in the XZ-plane. What can you say about its y-coordinate?

A point is on the x-axis. What are its y-coordinates and z-coordinates?

Find the equation of the circle with centre (0, 2) and radius 2

Solve 24x < 100, when
(i) x is a natural number. (ii) x is an integer.

Prove the following by using the principle of mathematical induction for all n ∈ N:

n (n + 1) (n + 5) is a multiple of 3.

Which of the following sentences are statements? Give reasons for your answer.

(i) There are 35 days in a month.

(ii) Mathematics is difficult.

(iii) The sum of 5 and 7 is greater than 10.

(iv) The square of a number is an even number.

(v) The sides of a quadrilateral have equal length.

(vi) Answer this question.

(vii) The product of (–1) and 8 is 8.

(viii) The sum of all interior angles of a triangle is 180°.

(ix) Today is a windy day.

(x) All real numbers are complex numbers.

An experiment consists of rolling a die and then tossing a coin once if the number on the die is even. If the number on the die is odd, the coin is tossed twice. Write the sample space for this experiment.

A coin is tossed. If it shows a tail, we draw a ball from a box which contains 2 red and 3 black balls. If it shows head, we throw a die. Find the sample space for this experiment.

Find the derivative of x² – 2 at x = 10.

Study Tips for Answering NCERT Questions:

NCERT questions are designed to test your understanding of the concepts and theories discussed in the chapter. Here are some tips to help you answer NCERT questions effectively:

Read the question carefully and focus on the core concept being asked.
Reference examples and data from the chapter when answering questions about Sequence and Series.
Review previous year question papers to get an idea of how such questions may be framed in exams.
Practice answering questions within the time limit to improve your speed and accuracy.
Discuss your answers with your teachers or peers to get feedback and improve your understanding.

Latest Blog Posts

Stay updated with our latest educational content and study tips

Smart Questions to Ask in a Parent-Teacher Meeting | PTM Made Easy

Parent-Teacher Meetings (PTMs) are more than quick updates on marks — they’re a chance to build a real partnership between home and school. A good Parent-Teacher Meeting conversation helps parents see beyond grades. It opens up insights about a child’s strengths, struggles, emotions and even hidden talents. When parents participate actively, they don’t just track […]

The Secret to Smarter Learning — Building Strong Critical Thinking Skills

In today’s world of endless information , knowing how to think is more important than knowing what to think . From school projects to real – life decisions , critical thinking helps students question ideas , analyze facts and form logical conclusions . But what exactly does critical thinking mean ? Simply put , it’s […]

Study Smarter, Not Harder: Build Productive Habits That Stick

Every student dreams of better grades , stronger focus and more study time – but the real challenge isn’t starting, it’s staying consistent . Building productive study habits is not about studying all day , it’s about studying smart . In today’s fast – paced digital world, distractions are everywhere – from endless phone notifications […]

The Hidden Risks of Online Gaming for Children — Is your child safe while gaming online?

Online gaming has rapidly become one of the most popular pastimes among children. Whether it’s multiplayer mobile games , PC adventures or console challenges , kids are spending more time than ever in the virtual world . On the surface, gaming seems entertaining and even educational – improving hand- eye coordination , teamwork and problem […]

View All Blog Posts