Chapter 5: Arithmetic Progressions (A.P.)
Unique Previous Year Questions extracted from the CBSE Class 10 Standard Mathematics 2025 question paper sets.
I
Multiple Choice Questions
1. Sum of \(m\) Terms
1 Mark
If the sum of first \(m\) terms of an AP is
\[
2m^2+3m,
\]
then its second term is:
Series 30/1/1 (Q11)
2. Common Difference
1 Mark
The 11th and 13th terms of an AP are 39 and 45, respectively.
What is the common difference of the AP?
Series 30/1/3 (Q17)
3. \(10^\text{th}\) Term of an AP
1 Mark
The 10th term of the AP
\[
5,\frac{19}{4},\frac{9}{2},\frac{17}{4},\ldots
\]
is:
Series 30/2/1 (Q15)
4. Term from the End
1 Mark
The 9th term from the end (towards first term) of the AP
\[
7,11,15,19,\ldots,147
\]
is:
Series 30/2/2 (Q2) & 30/2/3 (Q12)
5. Assertion – Reason
1 Mark
Assertion (A):
Common difference of the AP
\[
5,1,-3,-7,\ldots
\]
is 4.
Reason (R):
Common difference of the AP
\[
a_1,a_2,a_3,\ldots,a_n
\]
is obtained by
\[
d=a_n-a_{n-1}.
\]
6. Assertion – Reason
1 Mark
Assertion (A):
For an A.P.
\[
3,6,9,\ldots,198,
\]
the 10th term from the end is 168.
Reason (R):
If \(a\) and \(l\) are the first term and last term of an A.P.
with common difference \(d\), then the \(n\)-th term from the end
of the given A.P. is
\[
l-(n-1)d.
\]
II
Short Answer Type Questions
7. Sum of Three-Digit Multiples
3 Marks
Find the sum of all 3-digit natural numbers which are divisible
by 11.
Series 30/2/3 (Q27)
8. Simple Interest as an A.P.
3 Marks
A sum of ₹2,000 is invested at 7% per annum simple interest.
Calculate the interests at the end of 1st, 2nd and 3rd year.
Do these interests form an AP? If so, find the interest at the
end of the 27th year.
Series 30/2/1 (Q31) & 30/2/2 (Q28)
III
Long Answer Type Questions
9. Sum of First Sixteen Terms
5 Marks
The sum of the third term and the seventh term of an AP is 6
and their product is 8. Find the sum of the first sixteen terms
of the AP.
Series 30/3/1 (Q33a) & 30/3/3 (Q34a)
10. Find \(n\) and Sum of First 20 Terms
5 Marks
In an AP of \(n\) terms, the \(n\)-th term is 4 and the common
difference is 2. If the sum of its \(n\) terms is \(-14\), then
find \(n\). Also, find the sum of the first 20 terms.
Series 30/3/2 (Q32a)
11. First and Thirteenth Terms
5 Marks
The sum of the first six terms of an arithmetic progression is 42.
The ratio of the 10th term to the 30th term is \(1:3\).
Calculate the first and the thirteenth terms of the AP.
Series 30/3/2 (Q32b)
12. Ages in an A.P.
5 Marks
The minimum age for children to participate in a painting competition
is 8 years. It was observed that the youngest child was 8 years old
and the ages of participants were in an increasing order with a
common difference of 4 months. If the sum of the ages of all
participants was 168 years, find the age of the eldest participant
in the competition.
Series 30/3/1 (Q33b) & 30/3/3 (Q34b)
IV
Case Study Based Questions
13. Charity Run
4 Marks
A school plans a series of rounds around a track for a charity run.
The 1st round is 300 metres, and each subsequent round increases
by 50 metres. Total rounds planned are 10.
(i)
Write the fourth, fifth and sixth terms of the Arithmetic Progression
so formed. (1 mark)
(ii)
Determine the distance of the 8th round. (1 mark)
(iii) (a)
Find the total distance run after completing all 10 rounds.
(2 marks)
OR
(iii) (b)
If a runner completes only the first 6 rounds, what is the total
distance run by the runner? (2 marks)
14. Cable Cars
4 Marks
The distance of the first pole from the base point is 200 m, and
subsequent poles are installed at equal intervals of 150 m.
The total length of the cable car ride is 5000 m. The distance of
the last pole from the top is 300 m.
(i)
Find the distance of the 10th pole from the base.
(1 mark)
(ii)
Find the distance between the 15th pole and 25th pole.
(1 mark)
(iii) (a)
Find the time taken by the cable car to reach the 15th pole from
the top if it moves at 5 m/sec and starts from the top.
(2 marks)
OR
(iii) (b)
Find the total number of poles installed along the entire journey.
(2 marks)
15. Equilateral Triangle Grid
4 Marks
In an equilateral triangle of side 10 cm, small equilateral
triangles of side 1 cm are formed. Row 1 has one triangle,
Row 2 has three, Row 3 has five, and so on.
(i)
How many triangles will be there in the bottom-most row?
(1 mark)
(ii)
How many triangles will be there in the fourth row from the bottom?
(1 mark)
(iii) (a)
Find the total number of triangles of side 1 cm each till the 8th row.
(2 marks)
OR
(iii) (b)
How many more triangles are there from the 5th row to the 10th row
than in the first 4 rows? (2 marks)
16. Running Track
4 Marks
The length of the innermost lane (Lane 1) of an athletic track is
400 m, and each subsequent lane is 7.6 m longer than the preceding
lane.
(i)
What is the length of the 6th lane? (1 mark)
(ii)
How much longer is the 8th lane than the 4th lane?
(1 mark)
(iii) (a)
A student runs one round each in the first six lanes. Find the
total distance covered. (2 marks)
OR
(iii) (b)
A student runs one round each in Lane 4 to Lane 8. Find the
total distance covered. (2 marks)