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Saturday, 31 October

JEE Main · Maths · Sequences and Series

Sum of Finite AGP

JEE Main asked Sum of Finite AGP 3 times in 3 of the 108 shifts Lumi analysed, in 2022 and 2023. It belongs to Arithmetico-Geometric Series, in Sequences and Series (Maths). The longest wait between two years asking it was 1 year. In 2023 it came in more than one shift of the same year.

Updated 2026-10-24

Times asked
3
in 3 shifts
Years
2 of 8
First asked
2022
last in 2023
Pattern
Occasional
across the analysed shifts

Questions on this idea a shift, by year

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

00.10.20’170’200’210.04’220.14’230’240’250’26

Raw count: 2017: 0 in 1 shift · 2020: 0 in 12 shifts · 2021: 0 in 24 shifts · 2022: 1 in 24 shifts · 2023: 2 in 12 shifts · 2024: 0 in 18 shifts · 2025: 0 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
  • 20250 of 8
  • 20240 of 18
  • 20232 of 12
  • 20221 of 24
  • 20210 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.

  • Sum of finite arithmetico-geometric series
  • Sum of series with binomial-like weights

Difficulty

Easy 1Medium 1Hard 1

2 of the 3 questions had a numerical answer.

Every question

All 3 questions

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

  1. 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
  2. 6 Apr 2023, Shift 2 · Q23If (20)19+2(21)(20)18+3(21)2(20)17+…+20(21)19=k(20)19(20)^{19}+2(21)(20)^{18}+3(21)^2(20)^{17}+\ldots+20(21)^{19}=k(20)^{19}, then kk is equal to ___________.HardNumerical value
  3. 25 Jun 2022, Shift 2 · Q8The sum 1+2⋅3+3⋅32+.......+10⋅391 + 2 \cdot 3 + 3 \cdot 3^2 + ....... + 10 \cdot 3^9 is equal to :EasySingle correct

Shifts: 25 Jun 2022, Shift 2, 6 Apr 2023, Shift 2, 11 Apr 2023, Shift 1.

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