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Friday, 9 October

JEE Main Maths · Class 11

Sequences and Series: JEE Main previous year questions

Sequences and Series had 73 questions in the 42 JEE Main shifts Lumi analysed, about 1.6 a shift, asked in 42 of 42 shifts. It ranks 5 of 22 Maths chapters by questions; 18% of its questions were hard.

Questions
73
in 42 of 42 shifts
A shift, on average
1.6
of 25 Maths questions
Since 2024
-0.1
1.6 a shift in 2017–23, 1.6 in 2024–26
Numerical answer
19
26% of its questions

Year by year

How often it came

Questions in the analysed shifts of each year. Years differ in how many shifts Lumi analysed, so read the bars with the shift count.

Questions each year
08162’178’209’215’227’2314’2412’2516’26

2017: 1 shifts · 2020: 4 shifts · 2021: 4 shifts · 2022: 4 shifts · 2023: 4 shifts · 2024: 8 shifts · 2025: 8 shifts · 2026: 9 shifts

Difficulty by year
  • 20172
  • 20208
  • 20219
  • 20225
  • 20237
  • 202414
  • 202512
  • 202616
  • Easy
  • Medium
  • Hard

Inside the chapter

Topics and the ideas that repeat

4 topics and 20 distinct ideas; 10 ideas were asked more than once. Most questions are single correct and multi-step.

Topics, by questions

12 questions had no close topic in our taxonomy and are counted for the chapter only.

Ideas asked most
10 repeat

Study it on Lumi

Sequences and Series: the interactive lesson

Every question

All 73 Sequences and Series questions

Newest first. Each opens with its options and the official answer.

2026 16 questions

  1. 2 Apr 2026, Shift 1 · Q5Let AA be the set of first 101101 terms of an A.P., whose first term is 11 and the common difference is 55 and let BB be the set of…MediumSingle correct
  2. 2 Apr 2026, Shift 1 · Q22If ∑k=1nak=6n3\sum_{k=1}^{n}a_k=6n^3, then ∑k=16(ak+1−ak36)2\sum_{k=1}^{6}\left(\frac{a_{k+1}-a_k}{36}\right)^2 is equal to __________.MediumNumerical value
  3. 2 Apr 2026, Shift 2 · Q4Let a1,a2,a3,…a_1, a_2, a_3, \ldots be an A.P. and g1,g2,g3,…g_1, g_2, g_3, \ldots be an increasing G.P. If a1=a2+g2=1a_1 = a_2 + g_2 = 1 and a3+g3=4a_3 + g_3 = 4,…MediumSingle correct
  4. 2 Apr 2026, Shift 2 · Q5The sum 131+13+231+3+13+23+331+3+5+…\frac{1^3}{1} + \frac{1^3 + 2^3}{1 + 3} + \frac{1^3 + 2^3 + 3^3}{1 + 3 + 5} + \ldots up to 8 terms, is:MediumSingle correct
  5. 4 Apr 2026, Shift 1 · Q7The first term of an A.P. of 3030 non-negative terms is 103\frac{10}{3}. If the sum of this A.P. is the cube of its last term, then its…MediumSingle correct
  6. 4 Apr 2026, Shift 2 · Q7Let α=14+18+116+…∞\alpha=\frac14+\frac18+\frac1{16}+\ldots\infty and β=13+19+127+…∞\beta=\frac13+\frac19+\frac1{27}+\ldots\infty. Then the value of…EasySingle correct
  7. 5 Apr 2026, Shift 1 · Q2Let the sum of the first nn terms of an A.P. be 3n2+5n3n^2 + 5n. Then the sum of squares of the first 10 terms of the A.P. is:EasySingle correct
  8. 5 Apr 2026, Shift 1 · Q5∑n=110(528n(n+1)(n+2))\sum_{n=1}^{10}\left(\frac{528}{n(n+1)(n+2)}\right) is equal to:EasySingle correct
  9. 5 Apr 2026, Shift 2 · Q5If the sum of the first 10 terms of the series…HardSingle correct
  10. 5 Apr 2026, Shift 2 · Q6Let A1,A2,A3,……,A39A_1, A_2, A_3, \dots\dots, A_{39} be 39 arithmetic means between the numbers 59 and 159. Then the mean of A25,A28,A31A_{25}, A_{28}, A_{31}…EasySingle correct
  11. 6 Apr 2026, Shift 1 · Q5The value of 13−23+33−…+1531^3-2^3+3^3-\ldots+15^3 is:MediumSingle correct
  12. 6 Apr 2026, Shift 1 · Q6The sum of the first ten terms of an A.P. is 160 and the sum of the first two terms of a G.P. is 8. If the first term of the A.P. is equal…MediumSingle correct
  13. 6 Apr 2026, Shift 1 · Q24For the functions f(θ)=αtan⁡2θ+βcot⁡2θf(\theta)=\alpha\tan^2\theta+\beta\cot^2\theta, and g(θ)=αsin⁡2θ+βcos⁡2θg(\theta)=\alpha\sin^2\theta+\beta\cos^2\theta,…HardNumerical value
  14. 6 Apr 2026, Shift 2 · Q6The sum 1+12(12+22)+13(12+22+32)+…1+\frac{1}{2}\left(1^2+2^2\right)+\frac{1}{3}\left(1^2+2^2+3^2\right)+\ldots upto 10 terms is equal to :MediumSingle correct
  15. 8 Apr 2026, Shift 2 · Q5Let α=3+4+8+9+13+14+…\alpha = 3 + 4 + 8 + 9 + 13 + 14 + \ldots up to 40 terms. If (tan⁡β)α1020(\tan\beta)^{\frac{\alpha}{1020}} is a root of the equation…MediumSingle correct
  16. 8 Apr 2026, Shift 2 · Q25Let ff be a polynomial function such that…HardNumerical value

2025 12 questions

  1. 2 Apr 2025, Shift 1 · Q19Let a1,a2,a3,…a_1, a_2, a_3,\ldots be in an A.P. such that ∑k=112a2k−1=−725a1\sum_{k=1}^{12}a_{2k-1}=-\frac{72}{5}a_1, a1≠0a_1\neq0. If ∑k=1nak=0\sum_{k=1}^{n}a_k=0, then…MediumSingle correct
  2. 2 Apr 2025, Shift 2 · Q5The number of terms of an A.P. is even; the sum of all the odd terms is 24, the sum of all the even terms is 30 and the last term exceeds…MediumSingle correct
  3. 2 Apr 2025, Shift 2 · Q22If the sum of the first 10 terms of the series…HardNumerical value
  4. 3 Apr 2025, Shift 1 · Q6Let a1,a2,a3,…a_1, a_2, a_3, \ldots be a G.P. of increasing positive numbers. If a3a5=729a_3 a_5 = 729 and a2+a4=1114a_2 + a_4 = \frac{111}{4}, then…EasySingle correct
  5. 3 Apr 2025, Shift 1 · Q7The sum 1+3+11+25+45+71+…1 + 3 + 11 + 25 + 45 + 71 + \ldots upto 20 terms, is equal toMediumSingle correct
  6. 3 Apr 2025, Shift 2 · Q6The sum 1+1+32!+1+3+53!+1+3+5+74!+…1 + \frac{1+3}{2!} + \frac{1+3+5}{3!} + \frac{1+3+5+7}{4!} + \ldots upto ∞\infty terms, is equal toMediumSingle correct
  7. 4 Apr 2025, Shift 2 · Q5If the sum of the first 20 terms of the series…MediumSingle correct
  8. 4 Apr 2025, Shift 2 · Q6Consider two sets A and B, each containing three numbers in A.P. Let the sum and the product of the elements of A be 36 and p respectively…MediumSingle correct
  9. 7 Apr 2025, Shift 1 · Q6Let x1,x2,x3,x4x_1, x_2, x_3, x_4 be in a geometric progression. If 2,7,9,52, 7, 9, 5 are subtracted respectively from x1,x2,x3,x4x_1, x_2, x_3, x_4, then the…MediumSingle correct
  10. 7 Apr 2025, Shift 2 · Q6Let ana_n be the nthn^{\mathrm{th}} term of an A.P. If Sn=a1+a2+a3+…+an=700S_n=a_1+a_2+a_3+\ldots+a_n=700, a6=7a_6=7 and S7=7S_7=7, then ana_n is equal to :MediumSingle correct
  11. 7 Apr 2025, Shift 2 · Q7If the sum of the second, fourth and sixth terms of a G.P. of positive terms is 21 and the sum of its eighth, tenth and twelfth terms is…MediumSingle correct
  12. 8 Apr 2025, Shift 2 · Q6If 114+124+134+…∞=π490\frac{1}{1^4} + \frac{1}{2^4} + \frac{1}{3^4} + \ldots \infty = \frac{\pi^4}{90},…EasySingle correct

2024 14 questions

  1. 6 Apr 2024, Shift 2 · Q7A software company sets up mm number of computer systems to finish an assignment in 17 days. If 4 computer systems crashed on the start…MediumSingle correct
  2. 6 Apr 2024, Shift 2 · Q16Let ABCABC be an equilateral triangle. A new triangle is formed by joining the middle points of all sides of the triangle ABCABC and the…MediumSingle correct
  3. 8 Apr 2024, Shift 1 · Q25Let the positive integers be written in the form : 1 2 3 4 5 6 7 8 9 10 ... If the kthk^{\mathrm{th}} row contains exactly kk numbers for…MediumNumerical valueHas a figure
  4. 9 Apr 2024, Shift 1 · Q5If the sum of the series 11⋅(1+d)+1(1+d)(1+2d)+…+1(1+9d)(1+10d)\frac{1}{1\cdot(1+d)}+\frac{1}{(1+d)(1+2d)}+\ldots+\frac{1}{(1+9d)(1+10d)} is equal to 55, then 50d50d is equal…MediumSingle correct
  5. 9 Apr 2024, Shift 1 · Q26If a function ff satisfies f(m+n)=f(m)+f(n)f(m+n)=f(m)+f(n) for all m,n∈Nm,n\in\mathbf{N} and f(1)=1f(1)=1, then the largest natural number λ\lambda such…MediumNumerical value
  6. 9 Apr 2024, Shift 2 · Q1Let the range of the function f(x)=12+sin⁡3x+cos⁡3x, x∈Rf(x)=\frac{1}{2+\sin 3x+\cos 3x},\ x\in\mathbb{R} be [a,b][a, b]. If α\alpha and β\beta are respectively…MediumSingle correct
  7. 9 Apr 2024, Shift 2 · Q7Let a,ar,ar2,…a, ar, ar^2, \ldots be an infinite G.P. If ∑n=0∞arn=57\sum_{n=0}^{\infty}ar^n=57 and ∑n=0∞a3r3n=9747\sum_{n=0}^{\infty}a^3r^{3n}=9747, then a+18ra+18r is…MediumSingle correct
  8. 9 Apr 2024, Shift 2 · Q24If…HardNumerical value
  9. 29 Jan 2024, Shift 1 · Q6In an A.P., the sixth term a6=2a_6=2. If the product a1a4a5a_1a_4a_5 is the greatest, then the common difference of the A.P. is equal toHardSingle correct
  10. 29 Jan 2024, Shift 1 · Q7If 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…MediumSingle correct
  11. 30 Jan 2024, Shift 2 · Q6Let aa and bb be be two distinct positive real numbers. Let 11th11^{\mathrm{th}} term of a GP, whose first term is aa and third term is…EasySingle correct
  12. 30 Jan 2024, Shift 2 · Q25Let SnS_n be the sum to nn-terms of an arithmetic progression 3,7,11,…3, 7, 11, \ldots. If…MediumNumerical value
  13. 31 Jan 2024, Shift 1 · Q5The sum of the series 11−3⋅12+14+21−3⋅22+24+31−3⋅32+34+…\frac{1}{1-3\cdot1^2+1^4}+\frac{2}{1-3\cdot2^2+2^4}+\frac{3}{1-3\cdot3^2+3^4}+\ldots up to 10-terms isMediumSingle correct
  14. 31 Jan 2024, Shift 2 · Q7Let 2nd2^{nd}, 8th8^{th} and 44th44^{th} terms of a non-constant A. P. be respectively the 1st1^{st}, 2nd2^{nd} and 3rd3^{rd} terms of a G. P. If…MediumSingle correct

2023 7 questions

  1. 6 Apr 2023, Shift 1 · Q7The sum of the first 20 terms of the series 5+11+19+29+41+…5+11+19+29+41+\ldots isMediumSingle correct
  2. 6 Apr 2023, Shift 1 · Q8Let a1,a2,a3,…,ana_1,a_2,a_3,\ldots,a_n be nn positive consecutive terms of an arithmetic progression. If d>0d>0 is its common difference, then…MediumSingle correct
  3. 8 Apr 2023, Shift 2 · Q8Let ana_n be the nthn^{th} term of the series 5+8+14+23+35+50+…5 + 8 + 14 + 23 + 35 + 50 + \ldots and Sn=∑k=1nakS_n = \sum_{k=1}^{n} a_k. Then S30−a40S_{30} - a_{40}…MediumSingle correct
  4. 8 Apr 2023, Shift 2 · Q24Let 0<z<y<x0 < z < y < x be three real numbers such that 1x,1y,1z\frac{1}{x}, \frac{1}{y}, \frac{1}{z} are in an arithmetic progression and…HardNumerical value
  5. 11 Apr 2023, Shift 1 · Q5The number of integral solutions xx of log⁡(x+72)(x−72x−3)2≥0\log_{\left(x+\frac{7}{2}\right)}\left(\frac{x-7}{2x-3}\right)^2 \ge 0 isHardSingle correct
  6. 11 Apr 2023, Shift 1 · Q25Let S=109+1085+10752+…+25107+15108S = 109 + \frac{108}{5} + \frac{107}{5^2} + \ldots + \frac{2}{5^{107}} + \frac{1}{5^{108}}. Then the value of (16S−(25)−54)(16S - (25)^{-54})…MediumNumerical value
  7. 13 Apr 2023, Shift 2 · Q8Let a1,a2,a3,…a_1, a_2, a_3, \ldots be a G.P. of increasing positive numbers. Let the sum of its 6th6^{th} and 8th8^{th} terms be 22 and the…MediumSingle correct

2022 5 questions

  1. 25 Jul 2022, Shift 1 · Q24Let a, ba,\ b be two non-zero real numbers. If pp and rr are the roots of the equation x2−8ax+2a=0x^2-8ax+2a=0 and qq and ss are the roots of the…HardNumerical value
  2. 25 Jul 2022, Shift 1 · Q25Let a1=b1=1a_1=b_1=1, an=an−1+2a_n=a_{n-1}+2 and bn=an+bn−1b_n=a_n+b_{n-1} for every natural number n≥2n\ge2. Then ∑n=115an⋅bn\sum_{n=1}^{15}a_n\cdot b_n is equal to…MediumNumerical value
  3. 28 Jul 2022, Shift 1 · Q19Consider the sequence a1,a2,a3,…a_1,a_2,a_3,\ldots such that a1=1, a2=2a_1=1,\ a_2=2 and an+2=2an+1+ana_{n+2}=\frac{2}{a_{n+1}}+a_n for n=1,2,3,…n=1,2,3,\ldots. If…HardSingle correct
  4. 24 Jun 2022, Shift 1 · Q13If {ai}i=1n\{a_i\}_{i=1}^{n}, where n is an even integer, is an arithmetic progression with common difference 1, and ∑i=1nai=192\sum_{i=1}^{n} a_i = 192,…MediumSingle correct
  5. 29 Jun 2022, Shift 1 · Q12Let {an}n=0∞\{a_n\}_{n=0}^{\infty} be a sequence such that a0=a1=0a_0 = a_1 = 0 and an+2=2an+1−an+1a_{n+2} = 2a_{n+1} - a_n + 1 for all n≥0n \ge 0. Then,…MediumSingle correct

2021 9 questions

  1. 3 Aug 2021, Shift 2 · Q67If 'mm' is the arithmetic mean of two distinct real numbers ll and nn (l,n>1)(l, n > 1) and G1G_1, G2G_2 and G3G_3 are three geometric means…MediumSingle correct
  2. 3 Aug 2021, Shift 2 · Q83If the sum of all 3-digit numbers which are multiples of 9 is 41k41k, then 'kk' is equal to ‾\underline{\hspace{2em}}.EasyNumerical value
  3. 25 Jul 2021, Shift 1 · Q76Let SnS_n be the sum of the first n terms of an arithmetic progression. If S3n=3S2nS_{3n}=3S_{2n}, then the value of S4nS2n\frac{S_{4n}}{S_{2n}} is :EasySingle correct
  4. 25 Jul 2021, Shift 1 · Q84If the value of…MediumNumerical value
  5. 16 Mar 2021, Shift 2 · Q89Let 116\frac{1}{16}, a and b be in G.P. and 1a,1b\frac1a,\frac1b, 6 be in A.P., where a,b>0a,b>0. Then 72(a+b)72(a+b) is equal to ________.MediumNumerical value
  6. 16 Mar 2021, Shift 2 · Q90Let Sn(x)=log⁡a1/2x+log⁡a1/3x+log⁡a1/6x+log⁡a1/11x+log⁡a1/18x+log⁡a1/27x+…S_n(x)=\log_{a^{1/2}}x+\log_{a^{1/3}}x+\log_{a^{1/6}}x+\log_{a^{1/11}}x+\log_{a^{1/18}}x+\log_{a^{1/27}}x+\ldots up to n-terms,…HardNumerical value
  7. 18 Mar 2021, Shift 1 · Q67The value of 3+14+13+14+13+⋯∞3+\cfrac{1}{4+\cfrac{1}{3+\cfrac{1}{4+\cfrac{1}{3+\cdots\infty}}}} is equal to :MediumSingle correct
  8. 18 Mar 2021, Shift 1 · Q68132−1+152−1+172−1+…+1(201)2−1\frac{1}{3^2-1}+\frac{1}{5^2-1}+\frac{1}{7^2-1}+\ldots+\frac{1}{(201)^2-1} is equal to :MediumSingle correct
  9. 18 Mar 2021, Shift 1 · Q89The missing value in the following figure is __________.HardNumerical valueHas a figure

2020 8 questions

  1. 8 Jan 2020, Shift 1 · Q56Let f:R→Rf:\mathbf{R}\to\mathbf{R} be such that for all x∈Rx\in\mathbf{R}, (21+x+21−x)(2^{1+x}+2^{1-x}), f(x)f(x) and (3x+3−x)(3^x+3^{-x}) are in A.P., then…MediumSingle correct
  2. 8 Jan 2020, Shift 1 · Q73The sum ∑k=120(1+2+3+…+k)\displaystyle\sum_{k=1}^{20}(1+2+3+\ldots+k) is ______.EasyNumerical value
  3. 9 Jan 2020, Shift 2 · Q57Let ana_n be the nthn^{\mathrm{th}} term of a G.P. of positive terms. If ∑n=1100a2n+1=200\sum_{n=1}^{100}a_{2n+1}=200 and ∑n=1100a2n=100\sum_{n=1}^{100}a_{2n}=100,…MediumSingle correct
  4. 9 Jan 2020, Shift 2 · Q69If x=∑n=0∞(−1)ntan⁡2nθx=\sum_{n=0}^{\infty}(-1)^n\tan^{2n}\theta and y=∑n=0∞cos⁡2nθy=\sum_{n=0}^{\infty}\cos^{2n}\theta, for 0<θ<π40<\theta<\frac{\pi}{4}, then :EasySingle correct
  5. 9 Jan 2020, Shift 2 · Q72The number of terms common to the two A.P.'s 3,7,11,…,4073,7,11,\ldots,407 and 2,9,16,…,7092,9,16,\ldots,709 is ______.MediumNumerical value
  6. 2 Sep 2020, Shift 1 · Q57The sum of the first three terms of a G.P. is SS and their product is 27. Then all such SS lie in :MediumSingle correct
  7. 2 Sep 2020, Shift 1 · Q58If ∣x∣<1|x|<1, ∣y∣<1|y|<1 and x≠yx\neq y, then the sum to infinity of the following series…MediumSingle correct
  8. 6 Sep 2020, Shift 2 · Q56The common difference of the A.P. b1,b2,…,bmb_1, b_2, \ldots, b_m is 2 more than the common difference of A.P. a1,a2,…,ana_1, a_2, \ldots, a_n. If…MediumSingle correct

2017 2 questions

  1. 2 Apr 2017 (offline) · Q68For any three positive real numbers a, b and c, 9(25a2+b2)+25(c2−3ac)=15b(3a+c)9(25a^2+b^2)+25(c^2-3ac)=15b(3a+c). Then :HardSingle correct
  2. 2 Apr 2017 (offline) · Q69Let a,b,c∈Ra,b,c\in\mathbf{R}. If f(x)=ax2+bx+cf(x)=ax^2+bx+c is such that a+b+c=3a+b+c=3 and f(x+y)=f(x)+f(y)+xy, ∀ x,y∈Rf(x+y)=f(x)+f(y)+xy,\ \forall\ x,y\in\mathbf{R}, then…MediumSingle correct

Pattern: Asked most years.