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JEE Mains Previous Year Questions 
(2021-2024): Sequences and Series 
2024 
Q1 - 2024 (01 Feb Shift 1) 
Let 3 , a , b , c be in A.P. and 3 , a - 1 , b + 1 , c + 9 be in G.P. Then, the arithmetic mean of 
?? , ?? and ?? is : 
(1) -4 
(2) -1 
(3) 13 
(4) 11 
Q2 - 2024 (01 Feb Shift 1) 
Let 3 , 7 , 11 , 15 , … , 403 and 2 , 5 , 8 , 11 , … , 404 be two arithmetic progressions. Then the sum, 
of the common terms in them, is equal to 
Q3 - 2024 (01 Feb Shift 2) 
Let ?? ?? denote the sum of the first ?? terms of an arithmetic progression. If ?? 10
= 390 and 
the ratio of the tenth and the fifth terms is 15 : 7, then ?? 15
- ?? 5
 is equal to: 
(1) 800 
(2) 890 
(3) 790 
(4) 690 
Q4 - 2024 (01 Feb Shift 2) 
If three successive terms of a G.P. with common ratio ?? ( ?? > 1 ) are the lengths of the 
sides of a triangle and [ ?? ] denotes the greatest integer less than or equal to ?? , then 
3 [ ?? ] + [ - ?? ] is equal to : 
Q5 - 2024 (27 Jan Shift 1) 
The number of common terms in the progressions 4 , 9 , 14 , 19 , … …, up to 25
th 
 term and 
3 , 6 , 9 , 12, up to 37
th 
 term is : 
Page 2


JEE Mains Previous Year Questions 
(2021-2024): Sequences and Series 
2024 
Q1 - 2024 (01 Feb Shift 1) 
Let 3 , a , b , c be in A.P. and 3 , a - 1 , b + 1 , c + 9 be in G.P. Then, the arithmetic mean of 
?? , ?? and ?? is : 
(1) -4 
(2) -1 
(3) 13 
(4) 11 
Q2 - 2024 (01 Feb Shift 1) 
Let 3 , 7 , 11 , 15 , … , 403 and 2 , 5 , 8 , 11 , … , 404 be two arithmetic progressions. Then the sum, 
of the common terms in them, is equal to 
Q3 - 2024 (01 Feb Shift 2) 
Let ?? ?? denote the sum of the first ?? terms of an arithmetic progression. If ?? 10
= 390 and 
the ratio of the tenth and the fifth terms is 15 : 7, then ?? 15
- ?? 5
 is equal to: 
(1) 800 
(2) 890 
(3) 790 
(4) 690 
Q4 - 2024 (01 Feb Shift 2) 
If three successive terms of a G.P. with common ratio ?? ( ?? > 1 ) are the lengths of the 
sides of a triangle and [ ?? ] denotes the greatest integer less than or equal to ?? , then 
3 [ ?? ] + [ - ?? ] is equal to : 
Q5 - 2024 (27 Jan Shift 1) 
The number of common terms in the progressions 4 , 9 , 14 , 19 , … …, up to 25
th 
 term and 
3 , 6 , 9 , 12, up to 37
th 
 term is : 
(1) 9 
(2) 5 
(3) 7 
(4) 8 
Q6 - 2024 (27 Jan Shift 1) 
If 
8 = 3 +
1
4
( 3 + ?? ) +
1
4
2
( 3 + 2 ?? ) +
1
4
3
( 3 + 3 ?? ) + ? 8, 
then the value of ?? is 
Q7 - 2024 (27 Jan Shift 2) 
The 20
th 
 term from the end of the progression 20 , 19
1
4
, 18
1
2
, 17
3
4
, … , - 129
1
4
 is :- 
(1) -118 
(2) -110 
(3) -115 
(4) -100 
Q8 - 2024 (29 Jan Shift 1) 
If in a G.P. of 64 terms, the sum of all the terms is 7 times the sum of the odd terms of 
the G.P, then the common ratio of the G.P. is equal to 
(1) 7 
(2) 4 
(3) 5 
(4) 6 
Q9 - 2024 (29 Jan Shift 1) 
In an A.P., the sixth terms ?? 6
= 2. If the ?? 1
?? 4
?? 5
 is the greatest, then the common 
difference of the A.P., is equal to 
(1) 
3
2
 
(2) 
8
5
 
Page 3


JEE Mains Previous Year Questions 
(2021-2024): Sequences and Series 
2024 
Q1 - 2024 (01 Feb Shift 1) 
Let 3 , a , b , c be in A.P. and 3 , a - 1 , b + 1 , c + 9 be in G.P. Then, the arithmetic mean of 
?? , ?? and ?? is : 
(1) -4 
(2) -1 
(3) 13 
(4) 11 
Q2 - 2024 (01 Feb Shift 1) 
Let 3 , 7 , 11 , 15 , … , 403 and 2 , 5 , 8 , 11 , … , 404 be two arithmetic progressions. Then the sum, 
of the common terms in them, is equal to 
Q3 - 2024 (01 Feb Shift 2) 
Let ?? ?? denote the sum of the first ?? terms of an arithmetic progression. If ?? 10
= 390 and 
the ratio of the tenth and the fifth terms is 15 : 7, then ?? 15
- ?? 5
 is equal to: 
(1) 800 
(2) 890 
(3) 790 
(4) 690 
Q4 - 2024 (01 Feb Shift 2) 
If three successive terms of a G.P. with common ratio ?? ( ?? > 1 ) are the lengths of the 
sides of a triangle and [ ?? ] denotes the greatest integer less than or equal to ?? , then 
3 [ ?? ] + [ - ?? ] is equal to : 
Q5 - 2024 (27 Jan Shift 1) 
The number of common terms in the progressions 4 , 9 , 14 , 19 , … …, up to 25
th 
 term and 
3 , 6 , 9 , 12, up to 37
th 
 term is : 
(1) 9 
(2) 5 
(3) 7 
(4) 8 
Q6 - 2024 (27 Jan Shift 1) 
If 
8 = 3 +
1
4
( 3 + ?? ) +
1
4
2
( 3 + 2 ?? ) +
1
4
3
( 3 + 3 ?? ) + ? 8, 
then the value of ?? is 
Q7 - 2024 (27 Jan Shift 2) 
The 20
th 
 term from the end of the progression 20 , 19
1
4
, 18
1
2
, 17
3
4
, … , - 129
1
4
 is :- 
(1) -118 
(2) -110 
(3) -115 
(4) -100 
Q8 - 2024 (29 Jan Shift 1) 
If in a G.P. of 64 terms, the sum of all the terms is 7 times the sum of the odd terms of 
the G.P, then the common ratio of the G.P. is equal to 
(1) 7 
(2) 4 
(3) 5 
(4) 6 
Q9 - 2024 (29 Jan Shift 1) 
In an A.P., the sixth terms ?? 6
= 2. If the ?? 1
?? 4
?? 5
 is the greatest, then the common 
difference of the A.P., is equal to 
(1) 
3
2
 
(2) 
8
5
 
(3) 
2
3
 
(4) 
5
8
 
Q10 - 2024 (29 Jan Shift 2) 
If log
?? ? ?? , log
?? ? ?? , log
?? ? ?? are in an A.P. and log
?? ? ?? - log
?? ? 2 ?? , log
?? ? 2 ?? - log
?? ? 3 ?? , log
?? ? 3 ?? - log
?? ? ?? 
are also in an A.P, then a : b : c is equal to 
(1) 9 : 6 : 4 
(2) 16 : 4 : 1 
(3) 25 : 10 : 4 
(4) 6 : 3 : 2 
Q11 - 2024 (29 Jan Shift 2) 
If each term of a geometric progression ?? 1
, ?? 2
, ?? 3
, … with a
1
=
1
8
 and a
2
? a
1
, is the 
arithmetic mean of the next two terms and ?? ?? = ?? 1
+ ?? 2
+ ? + ?? ?? , then ?? 20
- ?? 18
 is equal 
to 
(1) 2
15
 
(2) - 2
18
 
(3) 2
18
 
(4) - 2
15
 
Q12 - 2024 (30 Jan Shift 1) 
Let ?? ?? denote the sum of first ?? terms an arithmetic progression. If ?? 20
= 790 and 
?? 10
= 145, then ?? 15
- ?? 5
 is 
(1) 395 
(2) 390 
(3) 405 
(4) 410 
Q13 - 2024 (30 Jan Shift 1) 
Let ?? = 1
2
+ 4
2
+ 8
2
+ 13
2
+ 19
2
+ 26
2
+ ? upto 10 terms and ?? = ?
?? = 1
10
? ?? 4
. If 4 ?? - ?? =
55 ?? + 40, then k is equal to 
Page 4


JEE Mains Previous Year Questions 
(2021-2024): Sequences and Series 
2024 
Q1 - 2024 (01 Feb Shift 1) 
Let 3 , a , b , c be in A.P. and 3 , a - 1 , b + 1 , c + 9 be in G.P. Then, the arithmetic mean of 
?? , ?? and ?? is : 
(1) -4 
(2) -1 
(3) 13 
(4) 11 
Q2 - 2024 (01 Feb Shift 1) 
Let 3 , 7 , 11 , 15 , … , 403 and 2 , 5 , 8 , 11 , … , 404 be two arithmetic progressions. Then the sum, 
of the common terms in them, is equal to 
Q3 - 2024 (01 Feb Shift 2) 
Let ?? ?? denote the sum of the first ?? terms of an arithmetic progression. If ?? 10
= 390 and 
the ratio of the tenth and the fifth terms is 15 : 7, then ?? 15
- ?? 5
 is equal to: 
(1) 800 
(2) 890 
(3) 790 
(4) 690 
Q4 - 2024 (01 Feb Shift 2) 
If three successive terms of a G.P. with common ratio ?? ( ?? > 1 ) are the lengths of the 
sides of a triangle and [ ?? ] denotes the greatest integer less than or equal to ?? , then 
3 [ ?? ] + [ - ?? ] is equal to : 
Q5 - 2024 (27 Jan Shift 1) 
The number of common terms in the progressions 4 , 9 , 14 , 19 , … …, up to 25
th 
 term and 
3 , 6 , 9 , 12, up to 37
th 
 term is : 
(1) 9 
(2) 5 
(3) 7 
(4) 8 
Q6 - 2024 (27 Jan Shift 1) 
If 
8 = 3 +
1
4
( 3 + ?? ) +
1
4
2
( 3 + 2 ?? ) +
1
4
3
( 3 + 3 ?? ) + ? 8, 
then the value of ?? is 
Q7 - 2024 (27 Jan Shift 2) 
The 20
th 
 term from the end of the progression 20 , 19
1
4
, 18
1
2
, 17
3
4
, … , - 129
1
4
 is :- 
(1) -118 
(2) -110 
(3) -115 
(4) -100 
Q8 - 2024 (29 Jan Shift 1) 
If in a G.P. of 64 terms, the sum of all the terms is 7 times the sum of the odd terms of 
the G.P, then the common ratio of the G.P. is equal to 
(1) 7 
(2) 4 
(3) 5 
(4) 6 
Q9 - 2024 (29 Jan Shift 1) 
In an A.P., the sixth terms ?? 6
= 2. If the ?? 1
?? 4
?? 5
 is the greatest, then the common 
difference of the A.P., is equal to 
(1) 
3
2
 
(2) 
8
5
 
(3) 
2
3
 
(4) 
5
8
 
Q10 - 2024 (29 Jan Shift 2) 
If log
?? ? ?? , log
?? ? ?? , log
?? ? ?? are in an A.P. and log
?? ? ?? - log
?? ? 2 ?? , log
?? ? 2 ?? - log
?? ? 3 ?? , log
?? ? 3 ?? - log
?? ? ?? 
are also in an A.P, then a : b : c is equal to 
(1) 9 : 6 : 4 
(2) 16 : 4 : 1 
(3) 25 : 10 : 4 
(4) 6 : 3 : 2 
Q11 - 2024 (29 Jan Shift 2) 
If each term of a geometric progression ?? 1
, ?? 2
, ?? 3
, … with a
1
=
1
8
 and a
2
? a
1
, is the 
arithmetic mean of the next two terms and ?? ?? = ?? 1
+ ?? 2
+ ? + ?? ?? , then ?? 20
- ?? 18
 is equal 
to 
(1) 2
15
 
(2) - 2
18
 
(3) 2
18
 
(4) - 2
15
 
Q12 - 2024 (30 Jan Shift 1) 
Let ?? ?? denote the sum of first ?? terms an arithmetic progression. If ?? 20
= 790 and 
?? 10
= 145, then ?? 15
- ?? 5
 is 
(1) 395 
(2) 390 
(3) 405 
(4) 410 
Q13 - 2024 (30 Jan Shift 1) 
Let ?? = 1
2
+ 4
2
+ 8
2
+ 13
2
+ 19
2
+ 26
2
+ ? upto 10 terms and ?? = ?
?? = 1
10
? ?? 4
. If 4 ?? - ?? =
55 ?? + 40, then k is equal to 
Q14 - 2024 (30 Jan Shift 2) 
Let ?? and ?? be be two distinct positive real numbers. Let 11
th 
 term of a GP, whose first 
term is ?? and third term is ?? , is equal to ?? th 
 term of another GP, whose first term is a and 
fifth term is ?? . Then p is equal to 
(1) 20 
(2) 25 
(3) 21 
(4) 24 
Q15 - 2024 (30 Jan Shift 2) 
Let ?? ?? be the sum to n-terms of an arithmetic progression 3 , 7 , 11 , … … 
If 40 < (
6
?? ( ?? + 1 )
?
?? = 1
?? ? ?? ?? ) < 42, then ?? equals 
Q16 - 2024 (31 Jan Shift 1) 
The sum of the series 
1
1 - 3 · 1
2
+ 1
4
+
2
1 - 3 · 2
2
+ 2
4
+
3
1 - 3 · 3
2
+ 3
4
+ ? up to 10 terms is 
(1) 
45
109
 
(2) -
45
109
 
(3) 
55
109
 
(4) -
55
109
 
Q17 - 2024 (31 Jan Shift 2) 
Let 2
nd 
, 8
th 
 and 44
th 
, terms of a non-constant A.P. be respectively the 1
st 
, 2
nd 
 and 3
rd 
 
terms of G.P. If the first term of A.P. is 1 then the sum of first 20 terms is equal to- 
(1) 980 
(2) 960 
(3) 990 
(4) 970 
Page 5


JEE Mains Previous Year Questions 
(2021-2024): Sequences and Series 
2024 
Q1 - 2024 (01 Feb Shift 1) 
Let 3 , a , b , c be in A.P. and 3 , a - 1 , b + 1 , c + 9 be in G.P. Then, the arithmetic mean of 
?? , ?? and ?? is : 
(1) -4 
(2) -1 
(3) 13 
(4) 11 
Q2 - 2024 (01 Feb Shift 1) 
Let 3 , 7 , 11 , 15 , … , 403 and 2 , 5 , 8 , 11 , … , 404 be two arithmetic progressions. Then the sum, 
of the common terms in them, is equal to 
Q3 - 2024 (01 Feb Shift 2) 
Let ?? ?? denote the sum of the first ?? terms of an arithmetic progression. If ?? 10
= 390 and 
the ratio of the tenth and the fifth terms is 15 : 7, then ?? 15
- ?? 5
 is equal to: 
(1) 800 
(2) 890 
(3) 790 
(4) 690 
Q4 - 2024 (01 Feb Shift 2) 
If three successive terms of a G.P. with common ratio ?? ( ?? > 1 ) are the lengths of the 
sides of a triangle and [ ?? ] denotes the greatest integer less than or equal to ?? , then 
3 [ ?? ] + [ - ?? ] is equal to : 
Q5 - 2024 (27 Jan Shift 1) 
The number of common terms in the progressions 4 , 9 , 14 , 19 , … …, up to 25
th 
 term and 
3 , 6 , 9 , 12, up to 37
th 
 term is : 
(1) 9 
(2) 5 
(3) 7 
(4) 8 
Q6 - 2024 (27 Jan Shift 1) 
If 
8 = 3 +
1
4
( 3 + ?? ) +
1
4
2
( 3 + 2 ?? ) +
1
4
3
( 3 + 3 ?? ) + ? 8, 
then the value of ?? is 
Q7 - 2024 (27 Jan Shift 2) 
The 20
th 
 term from the end of the progression 20 , 19
1
4
, 18
1
2
, 17
3
4
, … , - 129
1
4
 is :- 
(1) -118 
(2) -110 
(3) -115 
(4) -100 
Q8 - 2024 (29 Jan Shift 1) 
If in a G.P. of 64 terms, the sum of all the terms is 7 times the sum of the odd terms of 
the G.P, then the common ratio of the G.P. is equal to 
(1) 7 
(2) 4 
(3) 5 
(4) 6 
Q9 - 2024 (29 Jan Shift 1) 
In an A.P., the sixth terms ?? 6
= 2. If the ?? 1
?? 4
?? 5
 is the greatest, then the common 
difference of the A.P., is equal to 
(1) 
3
2
 
(2) 
8
5
 
(3) 
2
3
 
(4) 
5
8
 
Q10 - 2024 (29 Jan Shift 2) 
If log
?? ? ?? , log
?? ? ?? , log
?? ? ?? are in an A.P. and log
?? ? ?? - log
?? ? 2 ?? , log
?? ? 2 ?? - log
?? ? 3 ?? , log
?? ? 3 ?? - log
?? ? ?? 
are also in an A.P, then a : b : c is equal to 
(1) 9 : 6 : 4 
(2) 16 : 4 : 1 
(3) 25 : 10 : 4 
(4) 6 : 3 : 2 
Q11 - 2024 (29 Jan Shift 2) 
If each term of a geometric progression ?? 1
, ?? 2
, ?? 3
, … with a
1
=
1
8
 and a
2
? a
1
, is the 
arithmetic mean of the next two terms and ?? ?? = ?? 1
+ ?? 2
+ ? + ?? ?? , then ?? 20
- ?? 18
 is equal 
to 
(1) 2
15
 
(2) - 2
18
 
(3) 2
18
 
(4) - 2
15
 
Q12 - 2024 (30 Jan Shift 1) 
Let ?? ?? denote the sum of first ?? terms an arithmetic progression. If ?? 20
= 790 and 
?? 10
= 145, then ?? 15
- ?? 5
 is 
(1) 395 
(2) 390 
(3) 405 
(4) 410 
Q13 - 2024 (30 Jan Shift 1) 
Let ?? = 1
2
+ 4
2
+ 8
2
+ 13
2
+ 19
2
+ 26
2
+ ? upto 10 terms and ?? = ?
?? = 1
10
? ?? 4
. If 4 ?? - ?? =
55 ?? + 40, then k is equal to 
Q14 - 2024 (30 Jan Shift 2) 
Let ?? and ?? be be two distinct positive real numbers. Let 11
th 
 term of a GP, whose first 
term is ?? and third term is ?? , is equal to ?? th 
 term of another GP, whose first term is a and 
fifth term is ?? . Then p is equal to 
(1) 20 
(2) 25 
(3) 21 
(4) 24 
Q15 - 2024 (30 Jan Shift 2) 
Let ?? ?? be the sum to n-terms of an arithmetic progression 3 , 7 , 11 , … … 
If 40 < (
6
?? ( ?? + 1 )
?
?? = 1
?? ? ?? ?? ) < 42, then ?? equals 
Q16 - 2024 (31 Jan Shift 1) 
The sum of the series 
1
1 - 3 · 1
2
+ 1
4
+
2
1 - 3 · 2
2
+ 2
4
+
3
1 - 3 · 3
2
+ 3
4
+ ? up to 10 terms is 
(1) 
45
109
 
(2) -
45
109
 
(3) 
55
109
 
(4) -
55
109
 
Q17 - 2024 (31 Jan Shift 2) 
Let 2
nd 
, 8
th 
 and 44
th 
, terms of a non-constant A.P. be respectively the 1
st 
, 2
nd 
 and 3
rd 
 
terms of G.P. If the first term of A.P. is 1 then the sum of first 20 terms is equal to- 
(1) 980 
(2) 960 
(3) 990 
(4) 970 
 
Answer Key 
Q1 (4)  Q2 (6699) Q3 (3)  Q4 (1) 
Q5 (3)  Q6 (9) Q7 (3)  Q8 (4) 
Q9 (2)  ?? ?? ?? ( ?? ) Q11 (4)  Q12 (1) 
???? ( ?????? ) Q14 (3) Q15 (9) Q16 (4) 
Q17 (4) 
 
   
 
Solutions 
Q1 
3 , a , b , c ? A.P ? ? 3 , 3 + d , 3 + 2 d , 3 + 3 d 
3 , a - 1 , b + 1 , c + 9 ? G.P ? 3 , 2 + d , 4 + 2 d , 12 + 3 d 
a = 3 + d ? ( 2 + ?? )
2
= 3 ( 4 + 2 ?? ) 
b = 3 + 2 d ? d = 4 , - 2 
c = 3 + 3 d 
If d = 4 G.P ? 3 , 6 , 12 , 24 
a = 7 
b = 11 
c = 15 
?? + ?? + ?? 3
= 11 
Q2 
3 , 7 , 11 , 15 , … … , 403 
2 , 5 , 8 , 11 , … , 404 
L CM ? ( 4 , 3 ) = 12 
11 , 23 , 35 , … .. let (403)
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FAQs on Sequences and Series: JEE Mains Previous Year Questions (2021-2024) - Mathematics (Maths) for JEE Main & Advanced

1. How to find the sum of an arithmetic series?
Ans. To find the sum of an arithmetic series, you can use the formula \( S_n = \frac{n}{2} [2a + (n-1)d] \), where \(S_n\) is the sum of the series, \(n\) is the number of terms, \(a\) is the first term, and \(d\) is the common difference.
2. What is the general formula for the nth term of an arithmetic sequence?
Ans. The general formula for the nth term of an arithmetic sequence is \(a_n = a_1 + (n-1)d\), where \(a_n\) is the nth term, \(a_1\) is the first term, \(n\) is the term number, and \(d\) is the common difference.
3. How to find the sum of a geometric series?
Ans. To find the sum of a geometric series, you can use the formula \(S_n = \frac{a(1-r^n)}{1-r}\), where \(S_n\) is the sum of the series, \(a\) is the first term, \(r\) is the common ratio, and \(n\) is the number of terms.
4. What is the formula for the nth term of a geometric sequence?
Ans. The formula for the nth term of a geometric sequence is \(a_n = a_1 r^{n-1}\), where \(a_n\) is the nth term, \(a_1\) is the first term, \(r\) is the common ratio, and \(n\) is the term number.
5. How do you determine if a sequence is arithmetic or geometric?
Ans. To determine if a sequence is arithmetic, check if the difference between consecutive terms is constant. If the difference is constant, it is an arithmetic sequence. To determine if a sequence is geometric, check if the ratio of consecutive terms is constant. If the ratio is constant, it is a geometric sequence.
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