Are these practice questions for Sequences and Series based on the CBSE pattern?

Yes. Every practice question is modeled on the CBSE Class 11 - Science Mathematics exam pattern — including MCQs, assertion-reason questions, and short-answer formats that frequently appear in CBSE papers.

Are the practice questions for Sequences and Series free?

Yes. Every chapter includes free practice questions for Class 11 - Science students to get you started.

What types of questions are included?

The practice set for Sequences and Series mainly includes MCQs and CBSE-style short-answer questions, with instant feedback on each answer. For full-length textbook practice, use the NCERT Solutions page.

Are the practice questions suitable for board exam preparation?

Yes. The questions test the same concepts and depth that CBSE asks in board exams. After finishing, also solve the NCERT and NCERT Exemplar exercises for Sequences and Series for full coverage.

How many practice questions are there for Sequences and Series?

The number scales with chapter length and concept density. Each chapter typically has 15-50 practice questions across MCQ and short-answer formats.

Sequences and Series Class 11 Mathematics Practice Questions with Answers

easy

A sequence is defined by the formula

a_n = \frac{(-1)^n n^2}{n+1}

. Calculate the value of the 4th term,

a_4

.

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easy

State the formula for the

n^{\text{th}}

term of a Geometric Progression (G.P.).

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easy

Explain the difference between a finite sequence and an infinite sequence, providing one example for each.

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easy

Describe the method to determine if a given sequence is a Geometric Progression.

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easy

Identify the first term and the common ratio of the Geometric Progression:

3, -6, 12, \ldots

.

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easy

The first term of a Geometric Progression is

\sqrt{2}

and the common ratio is also

\sqrt{2}

. Calculate the 15th term of this progression.

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easy

Prove that if

a, b, c

are in G.P., then their logarithms,

\log a, \log b, \log c

, are in A.P. (Assume

a,b,c > 0

and the logarithm base is positive and not equal to 1).

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easy

Calculate the Geometric Mean (G.M.) between the numbers 4 and 16.

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easy

What is the primary difference between a sequence and a series?

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easy

Propose a method to determine if three given non-zero numbers

x, y, z

are in G.P. without explicitly calculating the common ratio.

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easy

Define a sequence in mathematics.

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easy

Calculate the sum of the first 8 terms of the geometric progression

3, 6, 12, \ldots

.

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medium

If

a, b, c

are in A.P. and

x, y, z

are in G.P., derive an expression for

x^{b-c} y^{c-a} z^{a-b}

and evaluate it.

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medium

A ball is dropped from a height of

H

meters. Each time it strikes the ground, it bounces back to

\frac{3}{4}

of the height from which it fell. Formulate a model for the total vertical distance traveled by the ball until it comes to rest and evaluate this distance for

H=16

meters.

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medium

Formulate an expression for the product

P

of the first

n

terms of a G.P. with first term

a

and common ratio

r

. Justify your formula.

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medium

Write the series

3 + 9 + 27 + \ldots + 3^n

using sigma notation.

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medium

The sum of

n

terms of a sequence is given by

S_n = 5n^2 - 3n

. Justify that the sequence is an A.P. and formulate a rule for its

k^{th}

term.

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medium

The first term of a G.P. is 81 and its fourth term is 3. Calculate the common ratio.

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medium

Critique the statement: "The geometric mean of two distinct positive numbers is always smaller than their arithmetic mean."

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medium

Define the Geometric Mean (G.M.) of two positive numbers

a

and

b

.

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medium

The sum of the first three terms of a G.P. is 21 and their product is 216. Analyze this information to find the three terms.

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medium

Insert four numbers between 5 and 160 so that the resulting sequence is a Geometric Progression.

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medium

If the numbers

x-1, x+1,

and

x+4

are the first three terms of a G.P., calculate the value of

x

.

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medium

Three numbers whose sum is 15 are in A.P. If 1, 4, and 19 are added to them respectively, the resulting numbers are in G.P. Create a system of equations to find the original numbers and justify your solution.

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medium

List the first four terms of the sequence defined by the recurrence relation

a_1 = 4

and

a_n = 2a_{n-1} - 1

for

n > 1

.

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medium

Given the sequence

5, 10, 20, 40, \ldots

, identify the first term '

a

', the common ratio '

r

', and write the formula for its

n^{\text{th}}

term,

a_n

.

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medium

Summarize the relationship between the Arithmetic Mean (A.M.) and Geometric Mean (G.M.) for any two positive real numbers.

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medium

Explain the procedure to derive the formula for the sum of the first

n

terms of a Geometric Progression,

S_n

. Describe the two distinct cases based on the value of the common ratio

r

.

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medium

Describe the Fibonacci sequence. List its first 8 terms and explain the recurrence relation that generates it.

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medium

Find the first five terms of the sequence whose

n^{\text{th}}

term is given by

a_n = \frac{n^2 - 1}{n+2}

.

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medium

Justify whether a sequence of non-zero numbers can be both an Arithmetic Progression (A.P.) and a Geometric Progression (G.P.) simultaneously.

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medium

In a Geometric Progression, the 4th term is 54 and the 7th term is 1458. Calculate the first term and the common ratio.

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medium

Design a G.P. for which the sum of the first three terms is 26 and their product is 216. Find the first term and the common ratio.

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medium

The Arithmetic Mean (A.M.) between two positive numbers is 25 and their Geometric Mean (G.M.) is 15. Calculate the two numbers.

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medium

How many terms of the geometric series

2 + 6 + 18 + \ldots

are required to obtain a sum of 728?

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hard

Summarize the concept of a series. Explain what is meant by the 'sum of a series' and how it differs from the series itself. Provide an example of a finite series and state its sum.

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hard

Formulate a recurrence relation for a sequence where each term, starting from the third, is the sum of all preceding terms. Let the first term be

a_1=1

.

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hard

If the sum of the first

p

terms of an A.P. is

q

and the sum of the first

q

terms is

p

, prove that the sum of the first

(p+q)

terms is

-(p+q)

. Assume

p \neq q

.

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hard

Justify why the sum of an infinite G.P. with a common ratio

|r| \geq 1

(and first term

a \neq 0

) does not converge to a finite value.

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hard

The product of the first three terms of a G.P. is 1000. If we add 6 to its second term and 7 to its third term, the new terms form an A.P. Analyze the given conditions to find the G.P.

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hard

The sum of three numbers in a G.P. is 28. If we subtract 1, 1, and 5 from these numbers in that order, the resulting numbers form an A.P. Find the numbers in the G.P.

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hard

Let

S_1, S_2, S_3, \dots, S_p

be the sums of

p

infinite geometric series whose first terms are

1, 2, 3, \dots, p

respectively, and whose common ratios are

\frac{1}{2}, \frac{1}{3}, \frac{1}{4}, \dots, \frac{1}{p+1}

respectively. Create a formula for

S_k

and then prove that

S_1 + S_2 + S_3 + \dots + S_p = \frac{p(p+3)}{2}

.

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hard

A ball is dropped from a height of 81 meters. Each time it hits the ground, it rebounds to

\frac{2}{3}

of the height from which it fell. Calculate the total vertical distance traveled by the ball up to the moment it hits the ground for the 5th time.

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hard

Derive the condition for the roots of the cubic equation

x^3 - px^2 + qx - r = 0

to be in G.P. and justify your derivation.

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hard

Calculate the sum to

n

terms of the series

0.4 + 0.44 + 0.444 + \ldots

.

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Sequences and SeriesClass 11 Mathematics Practice Questions