Page 1
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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