CBSE 10th Maths 2024-2025
Chapter - 5 Arithmetic Progressions
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 2nd and 4th term of an arithmetic progression (AP) is 6.
Find the common difference of the AP. Show your work.
Answer. Represents the 2nd and 4th 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 2nd and 4th 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 7th 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.)
