CBSE Class 10 Maths 2024-25: Chapter 5 Arithmetic Progressions Important Competency-Based Questions with Answers; Download Free PDF

As the CBSE Class 10 board exams get closer, it’s important for students to understand the new exam pattern. Starting in the 2024-25 school year, CBSE will include 50% more competency-based questions. These questions will be both multiple choice and written, focusing on how to use what students have learned in real-life situations.

This article explores Chapter 5 Arithmetic Progressions. It highlights key competency-based questions and provides answers to help students succeed.

Understanding Competency-Based Questions in Chapter 5: Arithmetic Progressions

Competency-based questions are designed to see how well students can apply their knowledge in everyday life. They can come in different forms, such as case studies, true-false questions, gap-filling tasks, and long or short answer questions.

Competency-based questions in Chapter 5: Arithmetic Progressions go beyond memorization, encouraging critical thinking and problem-solving. These questions help students grasp concepts deeply by applying them to real-world scenarios.

CBSE Class 10 Maths Chapter 5: Arithmetic Progressions Important Competency-Based Questions

Multiple Choice Questions

Q.1 In a game, a player must gather 20 flags positioned 5 meters apart in a straight line. The starting point is 10 meters away from the first flag. The player starts from the starting point, collects the 20 flags and comes back to the starting point to complete one round.

What will be the total distance covered by a player upon completing one round?

1.105 m
2. 210 m
3. 220 m
4. 1150 m

Answer. 2

Q.2 Shown below are some squares whose sides form an arithmetic progression (AP).

(Note: The figures are not to scale.)

Which of these are also in AP?

i) The areas of these squares.
ii) The perimeters of these squares.
iii) The length of the diagonals of these squares.

1. only ii)
2. only i) and ii)
3. only ii) and iii)
4. all - i), ii) and iii)

Answer. 3

Q.3 Given below is an arithmetic progression. X and Y are unknown.

Answer. 3

Q.4 Which of the following are in Arithmetic progression?

i) 2, 12, 22, 32, 42, ...
ii) 1, 2, 4, 7, 11, 16, ...
iii) 7, 6.5, 6, 5.5, 5, ...

1. only i)
2. only i) and ii)
3. only i) and iii)
4. all - i), ii) and iii)

Answer. 3

Q.5 Given below is a pattern.

Answer. 3

Q.6 Vanshika decided to plant a certain number of seeds every month as a part of a gardening project. In the first month, she planted 5 flower seeds, and in the final month, she planted 50 flower seeds. Every month, she planted 3 more seeds than the previous month.

How many flower seeds did Vanshika plant in total?

1. 50
2. 103
3. 390
4. 440

Answer. 4

Q.7 A construction company is working on construction of new floors in an old building which already had 6 floors. During the first week, they completed 5 floors. Each subsequent week, they completed 3 more floors.

If this progression continues for 12 weeks, how many floors will the building have in total? 

1. 38
2. 44
3. 47
4. 258

Answer. 2

Q.8 Which term of the arithmetic progression (AP) 21, 18, 15, ... is 0?

1. 6th term
2. 7th term
3. 8th term
4. (the AP does not have 0 as any term)

Answer. 3

Free Response Questions

Q.9 John is renovating his house. He began by painting one wall, which took him 2 hours on the first day. Each subsequent day, he spends an additional 30 min on the renovation project.

On which day will he spend 12 hours of his day on the renovation? Show your work.

Answer. Finds the first term of the progression as 2 × 60 = 120 min and writes the common difference as 30 min.

Finds the time spent on the n th day as 12 × 60 = 720 min.

Writes the equation for the n th day as:

720 = 120 + ( n - 1) × 30

Solves the above equation to find that John will spend 12 hours of his day on the 21st day.

Q.10 How many three-digit numbers are smaller than 200 and divisible by 8? Find sum of these numbers. Show your work.

Answer. Writes the sequence of 3-digit numbers less than 200 divisible by 8 as 104, 112, 120,  ..., 192 and mentions that it forms an arithmetic progression (AP).

Assumes that the AP has n terms and writes the equation for the last term as:

192 = 104 + ( n - 1)8

Solves the above equation to find the total number of terms in the AP as 12.

Finds the sum of all terms of the AP as:

Q.11 The difference between the 5th and 10th terms of an arithmetic progression (AP) is 15.

If the first term is 4, find the common difference and the 15th term of the AP. Show your work.

Answer. Writes the 5th and 10th term of the arithmetic progression as ( a + 4 d ) and ( a + 9 d ), where a is the first term and d is the common difference of the AP.

Writes the difference of both the terms as 5 d or (-5 d ) and equates it with 15 to get the common difference as (3) or (-3).

Finds the 15th term of the AP as 46 or (-38). The working may look as follows:

case i) when a = 4, n = 15 and d = 3:

T₁₅ = 4 + (15 - 1) × 3 = 46

case ii) when a = 4, n = 15 and d = -3:

T₁₅ = 4 - (15 - 1) × 3 = -38

Q.12 The difference between the 2^nd and 4^th term of an arithmetic progression (AP) is 6.

Find the common difference of the AP. Show your work.

Answer. Represents the 2^nd and 4^th term of the AP as ( a + d ) and ( a + 3 d ) with the first term as a and common difference as d.

Finds the difference of 2^nd and 4^th term as ( a + 3 d ) - ( a + d ) = 2 d or ( a + d ) - ( a + 3 d ) = (-2 d ).

Concludes that the common difference can either be 3 or (-3).

Case Study based Questions

Answer the questions based on the given information

Isha is planning to grow her orchard. She wants to plant rows of fruit trees in a way that each row has more trees than the one before, following a specific pattern. Given below are the details of her plan:

i) The first row will have 5 trees.
ii) Each new row will have 3 more trees than the one before.
iii) There will be a total of 10 rows of trees.

Q.13 Calculate the number of trees in the 10th row of the orchard. Show your work.

Answer. Writes that the first row contains 5 trees, and each subsequent row has 3 more trees than the previous row.

Concludes that the given pattern is in AP, and identifies a as 5 and d as 3

Finds the number of trees in the 10th row as:

5 + (10 - 1) × 3 = 32

Q.14 What will be the total number of trees in the orchard after all 10 rows are planted? Show your work.

Answer. Uses the sum of an arithmetic series formula and writes:

Solves the above equation to get the total number of trees in the orchard after all 10 rows are planted as 185.

Q.15 Isha changed her plan by not planting in rows 5 and 6 to create a pathway for walking, without altering the pattern for the rows. All rows will have the same number of trees as before.

Calculate the number of trees now. Show your work.

Answer. Forms two APs such as :

Calculates the number of trees in the 7^th row as:
5 + (7 - 1) × 3 = 23

Finds total number of trees in AP₂ as :

Finds the total number of trees as 38 + 110 = 148 trees.

(Award full marks if students calculate total number of trees and subtract number of trees in Row 5 and 6.)

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