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Saturday, 31 October

JEE Main · Maths · Sequences and Series

Infinite GP Sum

JEE Main asked Infinite GP Sum 15 times in 15 of the 108 shifts Lumi analysed, in 2020, 2021, 2022, 2023, 2024 and 2026. It belongs to AP and GP, in Sequences and Series (Maths). The longest wait between two years asking it was 2 years. In 2020, 2021, 2022 and 2024 it came in more than one shift of the same year.

Updated 2026-10-24

Times asked
15
in 15 shifts
Years
6 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 and 2026. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift of 25 Maths questions.

00.150.30’170.25’200.14’210.14’220.07’230.09’240’250.11’26

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

Shift by shift

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

  • 20261 of 9
  • 20250 of 8
  • 20242 of 18
  • 20231 of 12
  • 20224 of 24
  • 20214 of 24
  • 20203 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.

  • Combined ap and gp conditions
  • Value from infinite gp sums and logs

Difficulty

Easy 2Medium 11Hard 2

3 of the 15 questions had a numerical answer.

Every question

All 15 questions

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

  1. 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
  2. 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
  3. 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
  4. 15 Apr 2023, Shift 1 · Q24If the sum of the series…HardNumerical value
  5. 28 Jun 2022, Shift 2 · Q25Let for n=1,2,…,50n=1, 2, \ldots, 50, SnS_n be the sum of the infinite geometric progression whose first term is n2n^2 and whose common ratio is…HardNumerical value
  6. 27 Jun 2022, Shift 1 · Q3If x=∑n=0∞anx=\sum_{n=0}^{\infty} a^n, y=∑n=0∞bny=\sum_{n=0}^{\infty} b^n, z=∑n=0∞cnz=\sum_{n=0}^{\infty} c^n, where a, b, c are in A.P. and ∣a∣<1|a|<1, ∣b∣<1|b|<1,…MediumSingle correct
  7. 26 Jun 2022, Shift 2 · Q3If A=∑n=1∞1(3+(−1)n)nA = \sum_{n=1}^{\infty} \frac{1}{(3 + (-1)^n)^n} and B=∑n=1∞(−1)n(3+(−1)n)nB = \sum_{n=1}^{\infty} \frac{(-1)^n}{(3 + (-1)^n)^n}, then AB\frac{A}{B} is…MediumSingle correct
  8. 27 Jul 2022, Shift 2 · Q7Let the sum of an infinite G.P., whose first term is a and the common ratio is r, be 5. Let the sum of its first five terms be…MediumSingle correct
  9. 25 Feb 2021, Shift 1 · Q64If 0<θ,ϕ<π20 < \theta, \phi < \frac{\pi}{2}, x=∑n=0∞cos⁡2nθx = \sum_{n=0}^{\infty} \cos^{2n}\theta, y=∑n=0∞sin⁡2nϕy = \sum_{n=0}^{\infty} \sin^{2n}\phi and…MediumSingle correct
  10. 24 Feb 2021, Shift 1 · Q65If e(cos⁡2x+cos⁡4x+cos⁡6x+…∞)log⁡e2e^{(\cos^2 x + \cos^4 x + \cos^6 x + \dots \infty)\log_e 2} satisfies the equation t2−9t+8=0t^2 - 9t + 8 = 0, then the value of…MediumSingle correct
  11. 27 Aug 2021, Shift 1 · Q64If for x,y∈Rx, y \in \mathbf{R}, x>0x>0, y=log⁡10x+log⁡10x1/3+log⁡10x1/9+…y=\log_{10}x+\log_{10}x^{1/3}+\log_{10}x^{1/9}+\dots upto ∞\infty terms and…MediumSingle correct
  12. 26 Aug 2021, Shift 1 · Q67If the sum of an infinite GP a,ar,ar2,ar3,…a, ar, ar^2, ar^3, \ldots is 15 and the sum of the squares of its each term is 150, then the sum of…MediumSingle correct
  13. 3 Sep 2020, Shift 1 · Q73The value of (0.16)log⁡2.5(13+132+133+… to ∞)(0.16)^{\log_{2.5}\left(\frac{1}{3}+\frac{1}{3^2}+\frac{1}{3^3}+\ldots\text{ to }\infty\right)} is equal to __________.MediumNumerical value
  14. 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
  15. 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

Shifts: 9 Jan 2020, Shift 2, 2 Sep 2020, Shift 1, 3 Sep 2020, Shift 1, 24 Feb 2021, Shift 1, 25 Feb 2021, Shift 1, 26 Aug 2021, Shift 1, 27 Aug 2021, Shift 1, 26 Jun 2022, Shift 2, 27 Jun 2022, Shift 1, 28 Jun 2022, Shift 2, 27 Jul 2022, Shift 2, 15 Apr 2023, Shift 1, 6 Apr 2024, Shift 2, 9 Apr 2024, Shift 2, 4 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