Are these practice questions for Arithmetic Progressions based on the CBSE pattern?

Yes. Every practice question is modeled on the CBSE Class 10 Mathematics exam pattern — including MCQs, assertion-reason questions, and short-answer formats that frequently appear in CBSE papers.

Are the practice questions for Arithmetic Progressions free?

Yes. Every chapter includes free practice questions for Class 10 students to get you started.

What types of questions are included?

The practice set for Arithmetic Progressions 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 Arithmetic Progressions for full coverage.

How many practice questions are there for Arithmetic Progressions?

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

Arithmetic Progressions Class 10 Mathematics Practice Questions with Answers

easy

To find the number of terms in the AP

7, 13, 19, \ldots, 205

, a student writes the equation

205 = 7 + (n) \times 6

. Critique this approach. Identify the error and provide the correct formulation to solve the problem.

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easy

A list of numbers is given by

a, a^2, a^3, \ldots

for

a \neq 0

and

a \neq 1

. Justify why this is not an Arithmetic Progression.

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easy

Name the general term of an AP.

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easy

Define an Arithmetic Progression (AP).

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easy

Recall the two formulas for the sum of the first

n

terms of an AP.

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easy

A sequence is defined by

a_n = 5

for all

n \ge 1

. Justify why this sequence is an Arithmetic Progression.

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easy

Apply the concept of an AP to find the common difference if the 3rd term is 12 and the 5th term is 20.

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easy

Consider the sequence

1^2, 2^2, 3^2, 4^2, \ldots

, which is

1, 4, 9, 16, \ldots

. This is not an AP. Propose a modification to the third term of this sequence so that the first three terms,

1, 4, \ldots

, form an AP. Justify your proposed value.

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easy

Calculate the 21st term of the Arithmetic Progression whose first term is

-5

and the common difference is

2.5

.

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easy

Apply the sum formula to find the sum of an AP with 15 terms, whose first term is 10 and last term is 80.

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easy

Recall the formula for the

n

th term (

a_n

) of an AP.

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easy

Identify the first term

a

and the common difference

d

for the AP:

3, 1, -1, -3, \ldots

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medium

Solve for the first term and the common difference of an AP where the 4th term is 11 and the sum of the 5th and 7th terms is 34.

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medium

In an auditorium, the seats are arranged in rows. The first row has 20 seats, the second row has 24 seats, the third row has 28 seats, and so on. If there are 30 rows in the auditorium, solve for the total number of seats.

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medium

A student claims that for the AP

5, 12, 19, \ldots

, the term

250

is a part of the sequence. Evaluate this claim by determining if the term number

n

is a positive integer. Justify your conclusion.

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medium

Identify the common difference for the AP:

-\frac{1}{2}, -\frac{1}{2}, -\frac{1}{2}, -\frac{1}{2}, \ldots

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medium

Using the formula

a_n = a + (n-1)d

, find the 20th term of the AP:

2, 7, 12, 17, \ldots

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medium

Calculate the sum of the first 20 terms of a sequence whose

n

th term is given by the formula

a_n = 5 - 2n

.

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medium

Explain how to determine if a given list of numbers forms an AP.

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medium

Compare the two APs:

3, 7, 11, 15, \ldots

and

63, 65, 67, 69, \ldots

. Solve for the value of

n

for which their

n

th terms are equal.

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medium

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

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medium

List the first four terms of the AP when the first term

a = 10

and the common difference

d = -3

.

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medium

Two APs have the same common difference. The first term of one is 3 and that of the other is 8. Evaluate the difference between their 10th terms and their 100th terms. Based on your findings, formulate a general statement about the difference between the

n

-th terms of two such APs.

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medium

Summarize the key properties of the common difference (

d

) in an AP.

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medium

Solve for the number of terms in the AP:

7, 13, 19, \ldots, 205

.

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medium

Evaluate the statement: "If the

p

-th term of an AP is

q

and the

q

-th term is

p

, then its common difference is always

-1

." Justify your answer with a proof.

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medium

Create an Arithmetic Progression with a positive first term and a negative common difference, such that its 8th term is the first negative term. State the first term and common difference you chose and justify your choice.

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medium

A manufacturer of mobile phones produced 800 units in the fourth year and 1130 units in the seventh year. Assuming that the production increases uniformly by a fixed number every year, calculate (i) the production in the first year, and (ii) the total production in the first 10 years.

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medium

Two students, Rohan and Priya, are asked to find the sum of the AP:

2, 5, 8, \ldots

up to 10 terms. Rohan calculates the 10th term first,

a_{10} = 2 + (10-1)3 = 29

, and then finds the sum as

S_{10} = \frac{10}{2}(2+29) = 155

. Priya directly calculates the sum as

S_{10} = \frac{10}{2}[2(2)+(10-1)3] = 155

. Critique both methods. Justify which method is more universally applicable and explain the potential pitfall of Rohan's method.

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medium

List the first five terms of an AP whose first term is

a = -1.25

and common difference is

d = -0.25

.

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medium

Examine if the sequence

\sqrt{3}, \sqrt{12}, \sqrt{27}, \sqrt{48}, \ldots

forms an Arithmetic Progression.

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medium

A spiral is made of successive semicircles, with centers alternately at A and B. The radii of the semicircles form an AP:

0.5 \text{ cm}, 1.0 \text{ cm}, 1.5 \text{ cm}, \ldots

. Formulate an expression for the total length of a spiral made up of 13 consecutive semicircles and evaluate this length. (Use

\pi = \frac{22}{7}

).

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medium

Apply your knowledge of APs to calculate the 10th term from the end of the AP:

4, 9, 14, \ldots, 254

.

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medium

Describe the general form of an AP and explain what each component represents.

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hard

The sum of the first

n

terms of a sequence is given by

S_n = 3n^2 + 5n

. Analyze this sequence to determine if it is an AP. If it is, calculate its common difference and its 10th term.

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hard

Analyze the following situation: A person repays a loan of ₹3250 by paying ₹20 in the first month and then increases the payment by ₹15 every month. Does the monthly payment form an AP? If so, calculate how many months it will take to clear the loan.

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hard

Solve for the number of terms of the AP

63, 60, 57, \ldots

that must be taken so that their sum is 693.

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hard

The sum of the first

n

terms of a sequence is given by the formula

S_n = 3n^2 - n

. Justify whether this sequence is an Arithmetic Progression. If it is, formulate the expression for its common difference.

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hard

Explain why the sequence

a, a^2, a^3, a^4, \ldots

(for

a \neq 0, 1

) is not an AP.

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hard

The sum of three consecutive terms in an AP is 21. The product of the first and the third term is 45. Formulate a pair of equations representing this situation, assuming the terms are

a-d, a, a+d

. Solve these equations to find the three terms.

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hard

Calculate the sum of all three-digit numbers which are divisible by 9.

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hard

The numbers 2 and 34 are the first and last terms of an AP. Propose a method to insert five numbers between 2 and 34 such that the entire sequence forms an AP. Find these five numbers.

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hard

Design a problem involving the angles of a quadrilateral where the angles are in an Arithmetic Progression. The problem should require the user to find all four angles, given a relationship that the largest angle is three times the smallest angle. Formulate and solve the problem you have designed.

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hard

Summarize the minimum information required to fully describe a unique Arithmetic Progression. Explain why knowing only one piece of information is insufficient.

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hard

Design a real-world savings plan problem for a student where the monthly savings form an Arithmetic Progression. Formulate a question based on your plan that requires calculating the total savings after 2 years (24 months), and then solve it. The initial monthly saving and the monthly increment must be realistic values.

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Arithmetic ProgressionsClass 10 Mathematics Practice Questions