Chapter 5: Arithmetic Progressions
Unique Previous Year Questions from the
CBSE Class 10 Basic Mathematics 2025
paper sets, covering the major question types of Arithmetic Progressions.
I
Multiple Choice Questions
1. Finding the Common Difference
1 Mark
In an A.P.,
\[
a_n-a_{n-4}=32.
\]
Its common difference is:
(A) \(-8\)
(B) \(8\)
(C) \(4n\)
(D) \(4\)
Set 430/4/3
2. Radical A.P. – Finding a Term
1 Mark
The 20th term of the A.P.
\[
10\sqrt2,\;6\sqrt2,\;2\sqrt2,\ldots
\]
is:
(A) \(-76+10\sqrt2\)
(B) \(-62\sqrt2\)
(C) \(-66\sqrt2\)
(D) \(86\sqrt2\)
Set 430/4/3
3. Radical A.P. – Variant
1 Mark
The 16th term of the A.P.
\[
5\sqrt3,\;2\sqrt3,\;-\sqrt3,\ldots
\]
is:
(A) \(-25\sqrt3\)
(B) \(-40\sqrt3\)
(C) \(50\sqrt3\)
(D) \(-45+5\sqrt3\)
Set 430/5/2
4. Fractional A.P. – Finding a Term
1 Mark
The 22nd term of the A.P.
\[
\frac32,\;\frac12,\;-\frac12,\;-\frac32,\ldots
\]
is:
(A) \(\frac{45}{2}\)
(B) \(-9\)
(C) \(-\frac{39}{2}\)
(D) \(-21\)
Set 430/6/1
5. Mixed Fractional A.P.
1 Mark
The 15th term of the A.P.
\[
\frac{13}{3},\;3,\;\frac53,\ldots
\]
is:
(A) \(23\)
(B) \(-\frac{53}{3}\)
(C) \(-11\)
(D) \(-\frac{43}{3}\)
Set 430/6/2
6. Sum Formula Property
1 Mark
If the sum of first \(n\) terms of an A.P. is
\[
S_n=\frac{n}{2}(3n+1),
\]
then the first term of the A.P. is:
(A) \(2\)
(B) \(\frac32\)
(C) \(4\)
(D) \(\frac52\)
Set 430/6/2
II
Short Answer Type Questions
7. Finding the Sum of an A.P.
3 Marks
Find the sum of the Arithmetic Progression:
\[
7,\;10\frac12,\;14,\ldots,84.
\]
Set 430/4/2
8. Analyzing the \(S_n\) Formula
3 Marks
If the sum of first \(n\) terms of an A.P. is
\[
S_n=\frac{n}{2}(2n+8),
\]
find its first term and common difference.
Hence, find the 15th term.
Set 430/4/2
9. Constructing an A.P.
3 Marks
Find the A.P. whose third term is \(16\) and seventh term exceeds
the fifth term by \(12\).
Also, find the sum of the first \(29\) terms of the A.P.
Set 430/6/2
10. Term Verification
3 Marks
An A.P. has \(n^{\text{th}}\) term
\[
a_n=5+2n.
\]
Find the sum of the first \(20\) terms.
Can \(52\) be a term of this A.P.?
Set 430/6/2
III
Case Study Based Questions
11. Figure-Based – Spiral Pattern
4 Marks
In a garden, saplings of rose flowers were planted at equal
intervals to form a spiral pattern. The spiral is made up of
successive semicircles of radii
\[
50\text{ cm},\;100\text{ cm},\;150\text{ cm},\ldots
\]
Spiral 1 has \(10\) flowers, Spiral 2 has \(20\) flowers,
Spiral 3 has \(30\) flowers and so on.
(i)
What is the radius of the 13th spiral?
(ii)
If the radius of the \(n^{\text{th}}\) spiral is \(500\) cm,
find the value of \(n\).
(iii)
Find the total number of saplings till the 11th spiral.
OR
Till which spiral will there be a total of \(450\) saplings?
Set 430/1/1
12. Financial Data – Loan Installments
4 Marks
A woman borrowed ₹\(10,00,000\) and promised to return it in
monthly instalments.
After one month, she returned ₹\(10,000\), the next month
₹\(15,000\), the third month ₹\(20,000\) and so on, increasing
the monthly instalment uniformly.
(i)
Find the amount of instalment paid in the tenth month.
(ii)
In which instalment did she pay ₹\(40,000\)?
(iii)
If she returned ₹\(11,50,000\) in all, how many instalments
did she pay?
OR
By which instalment had she returned a total amount of
₹\(3,25,000\)?
Set 430/2/1
13. Applied Scenario – Yoga Session
4 Marks
In a society park, yoga sessions were held daily. On day one,
\(5\) people joined. On day two, \(3\) more people joined.
On day three, another \(3\) people joined and in this manner
every next day, \(3\) more people kept on joining.
(i)
On which day did \(59\) people join the yoga session?
(ii)
How many people joined the yoga session on the 31st day?
(iii)
If the yoga instructor was paid ₹\(100\) for each person
attending, on which day would he earn ₹\(5,000\)?
OR
What was the total amount earned by the instructor in
\(16\) days?
Set 430/3/1
14. Figure-Based – Stacking Chairs
4 Marks
A tent house stacks chairs to save space. The height of the
first seat is \(44\) cm from ground level and the gap between
every two seats is \(10\) cm:
\[
h_1,h_2,h_3,\ldots
\]
(i)
Write the values of
\(h_1,h_2,h_3,h_4\) and \(h_5\).
(ii)
Show that the above values form an A.P. Write its first term
and common difference.
(iii)
If chairs can be stacked up to a maximum height of \(160\) cm,
find the maximum number of chairs in a stack.
OR
Is it possible to stack \(15\) chairs if the maximum height
cannot be more than \(180\) cm?
Set 430/5/1