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Saturday, 31 October

JEE Main · Maths · Sequences and Series

Sum of Infinite AGP

JEE Main asked Sum of Infinite AGP 5 times in 5 of the 108 shifts Lumi analysed, in 2021, 2022, 2024 and 2025. It belongs to Arithmetico-Geometric Series, in Sequences and Series (Maths). The longest wait between two years asking it was 2 years. In 2021 it came in more than one shift of the same year.

Updated 2026-10-24

Times asked
5
in 5 shifts
Years
4 of 8
First asked
2021
last in 2025
Pattern
Comes in cycles
across the analysed shifts

Questions on this idea a shift, by year

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

00.10.20’170’200.07’210.04’220’230.05’240.13’250’26

Raw count: 2017: 0 in 1 shift · 2020: 0 in 12 shifts · 2021: 2 in 24 shifts · 2022: 1 in 24 shifts · 2023: 0 in 12 shifts · 2024: 1 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
  • 20241 of 18
  • 20230 of 12
  • 20221 of 24
  • 20212 of 24
  • 20200 of 12
  • 20170 of 1

Asked in that shift More than once Not asked

How JEE Main framed it

Numerical value is the usual form. Skill tested: calculation.

  • Find unknown from infinite agp sum
  • Probability from pmf requiring infinite agp sum

Difficulty

Easy 1Medium 4Hard 0

3 of the 5 questions had a numerical answer.

Every question

All 5 questions

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

  1. 3 Apr 2025, Shift 2 · Q8If the probability that the random variable XX takes the value xx is given by P(X=x)=k(x+1)3−x, x=0,1,2,3…P(X = x) = k(x + 1)3^{-x},\ x = 0, 1, 2, 3\ldots, where…MediumSingle correct
  2. 27 Jan 2024, Shift 1 · Q24If 8=3+14(3+p)+142(3+2p)+143(3+3p)+⋯⋯∞8=3+\dfrac{1}{4}(3+p)+\dfrac{1}{4^2}(3+2p)+\dfrac{1}{4^3}(3+3p)+\cdots\cdots\infty, then the value of p is ________.MediumNumerical value
  3. 29 Jul 2022, Shift 1 · Q24Let a1,a2,a3,…a_1, a_2, a_3, \ldots be an A.P. If ∑r=1∞ar2r=4\sum_{r=1}^{\infty} \frac{a_r}{2^r} = 4, then 4a24a_2 is equal to __________.MediumNumerical value
  4. 25 Jul 2021, Shift 1 · Q84If the value of…MediumNumerical value
  5. 26 Feb 2021, Shift 1 · Q78The sum of the infinite series 1+23+732+1233+1734+2235+……1+\frac{2}{3}+\frac{7}{3^2}+\frac{12}{3^3}+\frac{17}{3^4}+\frac{22}{3^5}+\ldots\ldots is equal to :EasySingle correct

Shifts: 26 Feb 2021, Shift 1, 25 Jul 2021, Shift 1, 29 Jul 2022, Shift 1, 27 Jan 2024, Shift 1, 3 Apr 2025, Shift 2.

Same topic

Other ideas in Arithmetico-Geometric Series

Arithmetico-Geometric Series has 9 ideas JEE Main has asked; 6 of them came up in more than one question.

Topic analysisChapter analysisStudy this chapterAll repeated ideas