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Saturday, 31 October

JEE Main · Maths · Sequences and Series

Conditions for Three Terms in AP or GP

JEE Main asked Conditions for Three Terms in AP or GP 6 times in 6 of the 108 shifts Lumi analysed, in 2017, 2020, 2021, 2024 and 2025. It belongs to AP and GP, in Sequences and Series (Maths). The longest wait between two years asking it was 3 years, across 2018 and 2019, which Lumi has no shifts for. In 2024 it came in more than one shift of the same year.

Updated 2026-10-24

Times asked
6
in 6 shifts
Years
5 of 8
First asked
2017
last in 2025
Pattern
Asked most years
across the analysed shifts

Questions on this idea a shift, by year

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

00.510.86’170.08’200.03’210’220’230.09’240.13’250’26

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

Shift by shift

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

  • 20260 of 9
  • 20251 of 8
  • 20242 of 18
  • 20230 of 12
  • 20220 of 24
  • 20211 of 24
  • 20201 of 12
  • 20171 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.

  • Combined ap and gp conditions
  • Identify progression from algebraic condition

Difficulty

Easy 0Medium 5Hard 1

2 of the 6 questions had a numerical answer.

Every question

All 6 questions

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

  1. 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
  2. 1 Feb 2024, Shift 2 · Q23If three successive terms of a G.P. with common ratio rr (r>1r>1) are the lengths of the sides of a triangle and [r][r] denotes the…MediumNumerical value
  3. 1 Feb 2024, Shift 1 · Q6Let 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 a, b and c is :MediumSingle correct
  4. 4 Aug 2021, Shift 2 · Q86If 32, 5x5x and yy are in A.P., and 2, xx and yy are in G.P., then the positive common difference of the A.P. is ________.MediumNumerical value
  5. 5 Sep 2020, Shift 1 · Q56If 32sin⁡2α−13^{2\sin 2\alpha-1}, 14 and 34−2sin⁡2α3^{4-2\sin 2\alpha} are the first three terms of an A.P. for some α\alpha, then the sixth term of this…MediumSingle correct
  6. 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

Shifts: 2 Apr 2017 (offline), 5 Sep 2020, Shift 1, 4 Aug 2021, Shift 2, 1 Feb 2024, Shift 2, 1 Feb 2024, Shift 1, 7 Apr 2025, Shift 1.

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