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Saturday, 31 October

JEE Main · Maths · Sequences and Series

AP Sum of n terms

JEE Main asked AP Sum of n terms 31 times in 29 of the 108 shifts Lumi analysed, in 2020, 2021, 2022, 2023, 2024, 2025 and 2026. It belongs to AP and GP, in Sequences and Series (Maths). The longest wait between two years asking it was 1 year. In 2020, 2021, 2022, 2023, 2024, 2025 and 2026 it came in more than one shift of the same year.

Updated 2026-10-24

Times asked
31
in 29 shifts
Years
7 of 8
First asked
2020
last in 2026
Pattern
Asked most years
across the analysed shifts

Questions on this idea a shift, by year

2017–2026. Asked in 2020, 2021, 2022, 2023, 2024, 2025 and 2026. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift of 25 Maths questions.

00.30.60’170.42’200.17’210.14’220.21’230.38’240.25’250.44’26

Raw count: 2017: 0 in 1 shift · 2020: 5 in 12 shifts · 2021: 5 in 24 shifts · 2022: 4 in 24 shifts · 2023: 3 in 12 shifts · 2024: 8 in 18 shifts · 2025: 2 in 8 shifts · 2026: 4 in 9 shifts.

Shift by shift

Each square is one analysed shift, in date order. Open a filled one for that paper.

  • 20264 of 9
  • 20252 of 8
  • 20248 of 18
  • 202322 of 12
  • 20224 of 24
  • 20215 of 24
  • 202024 of 12
  • 20170 of 1

Asked in that shift More than once Not asked

How JEE Main framed it

Single correct is the usual form. Skill tested: multi-step.

  • Sum of series with summation general term
  • Ap sums from term ratio and sum

Difficulty

Easy 6Medium 24Hard 1

12 of the 31 questions had a numerical answer.

Every question

All 31 questions

From the official JEE Main shift papers, newest first. Open one for the full question, the options and the official answer.

  1. 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
  2. 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
  3. 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
  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. 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
  6. 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
  7. 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
  8. 30 Jan 2024, Shift 1 · Q6Let SnS_n denote the sum of first nn terms of an arithmetic progression. If S20=790S_{20}=790 and S10=145S_{10}=145, then S15−S5S_{15}-S_5 is :MediumSingle correct
  9. 1 Feb 2024, Shift 2 · Q7Let SnS_n denote the sum of the first nn terms of an arithmetic progression. If S10=390S_{10}=390 and the ratio of the tenth and the fifth…MediumSingle correct
  10. 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
  11. 8 Apr 2024, Shift 2 · Q23An arithmetic progression is written in the following way 2 5 8 11 14 17 20 23 26 29 _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _…MediumNumerical valueHas a figure
  12. 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
  13. 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
  14. 5 Apr 2024, Shift 1 · Q25Let a1,a2,a3,…a_1, a_2, a_3, \ldots be in an arithmetic progression of positive terms. Let…HardNumerical value
  15. 13 Apr 2023, Shift 1 · Q6Let s1,s2,s3,…,s10s_1, s_2, s_3, \ldots, s_{10} respectively be the sum to 12 terms of 10 A.P. s whose first terms are 1,2,3,…,101, 2, 3, \ldots, 10 and the…MediumSingle correct
  16. 13 Apr 2023, Shift 1 · Q24The sum to 20 terms of the series 2⋅22−32+2⋅42−52+2⋅62−……2\cdot2^2-3^2+2\cdot4^2-5^2+2\cdot6^2-\ldots\ldots is equal to ________.MediumNumerical value
  17. 10 Apr 2023, Shift 1 · Q26The sum of all those terms, of the arithmetic progression 3, 8, 13, ..., 373, which are not divisible by 3, is equal to ____________.EasyNumerical value
  18. 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
  19. 30 Jul 2022, Shift 2 · Q67For ∣α∣≥1|\alpha| \geq 1, let 54−2α5^{4-2\alpha}, 63, 52α−15^{2\alpha-1} be in A.P. with the common difference d. Let Sn\mathrm{S_n} denote the sum…MediumSingle correct
  20. 26 Jul 2022, Shift 1 · Q23The series of positive multiples of 3 is divided into sets : {3}\{3\}, {6, 9, 12}\{6,\ 9,\ 12\}, {15, 18, 21, 24, 27}\{15,\ 18,\ 21,\ 24,\ 27\}, …\ldots Then the…MediumNumerical value
  21. 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
  22. 18 Mar 2021, Shift 2 · Q73Let S1S_1 be the sum of first 2n2n terms of an arithmetic progression. Let S2S_2 be the sum of first 4n4n terms of the same arithmetic…MediumSingle correct
  23. 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
  24. 22 Jul 2021, Shift 2 · Q74Let Sn\mathrm{S}_\mathrm{n} denote the sum of first n-terms of an arithmetic progression. If S10=530\mathrm{S}_{10}=530, S5=140\mathrm{S}_5=140,…EasySingle correct
  25. 26 Aug 2021, Shift 2 · Q90Let a1,a2,…,a10\mathrm{a}_1,\mathrm{a}_2,\ldots,\mathrm{a}_{10} be an AP with common difference −3-3 and…MediumNumerical value
  26. 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
  27. 3 Sep 2020, Shift 2 · Q56If the sum of the series 20+1935+1915+1845+…20 + 19\frac{3}{5} + 19\frac{1}{5} + 18\frac{4}{5} + \ldots upto nthn^{th} term is 488 and the nthn^{th} term is…MediumSingle correct
  28. 3 Sep 2020, Shift 1 · Q56If the first term of an A.P. is 3 and the sum of its first 25 terms is equal to the sum of its next 15 terms, then the common difference…EasySingle correct
  29. 2 Sep 2020, Shift 2 · Q57If the sum of first 11 terms of an A.P., a1a_1, a2a_2, a3a_3, ... is 0 (a1≠0a_1 \neq 0), then the sum of the A.P., a1a_1, a3a_3, a5a_5, ...,…MediumSingle correct
  30. 2 Sep 2020, Shift 2 · Q58Let S be the sum of the first 9 terms of the series : {x+ka}+{x2+(k+2)a}+{x3+(k+4)a}+{x4+(k+6)a}+…\{x+ka\}+\{x^2+(k+2)a\}+\{x^3+(k+4)a\}+\{x^4+(k+6)a\}+\ldots where a≠0a \neq 0 and…MediumSingle correct
  31. 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

Shifts: 8 Jan 2020, Shift 1, 2 Sep 2020, Shift 2, 3 Sep 2020, Shift 2, 3 Sep 2020, Shift 1, 18 Mar 2021, Shift 2, 22 Jul 2021, Shift 2, 25 Jul 2021, Shift 1, 3 Aug 2021, Shift 2, 26 Aug 2021, Shift 2, 24 Jun 2022, Shift 1, 25 Jul 2022, Shift 1, 26 Jul 2022, Shift 1, 30 Jul 2022, Shift 2, 10 Apr 2023, Shift 1, 13 Apr 2023, Shift 1, 30 Jan 2024, Shift 2, 30 Jan 2024, Shift 1, 1 Feb 2024, Shift 2, 5 Apr 2024, Shift 1, 6 Apr 2024, Shift 2, 8 Apr 2024, Shift 2, 8 Apr 2024, Shift 1, 9 Apr 2024, Shift 1, 2 Apr 2025, Shift 1, 7 Apr 2025, Shift 2, 2 Apr 2026, Shift 2, 4 Apr 2026, Shift 1, 6 Apr 2026, Shift 1, 8 Apr 2026, Shift 2.

Same topic

Other ideas in AP and GP

AP and GP has 23 ideas JEE Main has asked; 16 of them came up in more than one question. The 12 most asked are below.

Topic analysisChapter analysisStudy this chapterAll repeated ideas