JEE Main · Maths · Sequences and Series
Arithmetico-Geometric Series: JEE Main previous year questions
22 questions in the 108 JEE Main shifts Lumi analysed, in 6 of 8 years. Pattern: Asked most years. 3 came in 2024–26. Here is how it is asked and which ideas come back.
- Questions
- 22
- in 22 of 108 shifts
- Years asked
- 6/8
- last asked 2025
- Weighted estimate
- 0.1
- model; history: 0.1 a shift on average, typically 0.0–0.2
Key findings
- 01
Asked in 6 of 8 years with analysed shifts and in 22 of 108 shifts: 22 questions, #134 of 196 topics. Last asked in 2025.
- 02
50% of its questions since 2020 tested an idea no earlier year had asked; 8 repeated an idea from the year before.
- 03
The most repeated idea is Sum of Infinite AGP, asked 5 times in 5 shifts (2021, 2022, 2024, 2025), most often as “find unknown from infinite agp sum”.
- 04
JEE Main has asked 9 of the 63 ideas in this topic; 51 have never been asked, directly or inside another question.
- 05
Mostly asked as single correct (50%); 50% need a numerical answer, 9% are easy and 32% hard.
- 06
The skill tested most is multi-step (59%), then calculation (41%).
Questions a shift, year by year
Out of the 25 Maths questions in a shift. Years differ in how many shifts Lumi analysed, so each year is scaled to one shift.
Raw count: 2017: 0 in 1 shift · 2020: 1 in 12 shifts · 2021: 5 in 24 shifts · 2022: 7 in 24 shifts · 2023: 6 in 12 shifts · 2024: 2 in 18 shifts · 2025: 1 in 8 shifts · 2026: 0 in 9 shifts.
- Up to 2023
- 0.2
- a shift, of 25
- Since 2024
- 0.1
- -0.1
- Usual gap
- 1.0 yrs
- between years asking it
- Shifts with it
- 22/108
- 20% of analysed shifts
How it is asked
Difficulty, format and skill
Across all 22 questions on Arithmetico-Geometric Series since 2017.
Difficulty
QUESTIONS- Easy2 · 9%
- Medium13 · 59%
- Hard7 · 32%
Format
SHARE- Single correct · 11 Q50%
- Numerical value · 11 Q50%
Skill tested
SHARE- Multi-step · 13 Q59%
- Calculation · 9 Q41%
Repeats
New idea, or one asked before?
Each column is a year. Blue questions tested an idea no earlier year had asked; navy ones went back to an idea from an earlier year. 2017 is the first year, so everything in it counts as new. Heights are question counts, and Lumi analysed 1 to 24 shifts a year, so compare the split inside a column rather than heights across years.
- Idea asked for the first time
- Idea asked in an earlier year
Coverage of the topic
JEE Main has asked 9 of the 63 ideas in this topic. 51 have never been asked yet.
- Asked directly9 · 14%
- Touched inside another question3 · 5%
- Never asked51 · 81%
Ideas come from Lumi’s JEE syllabus map. A never-asked idea is not a safe skip: across all of JEE Main, 22% of questions since 2024 tested an idea no earlier year had asked.
Drill down
Chapter, idea, question
Every idea JEE Main tested in this topic, with its eight years. Open one to read the questions.
7 ideas inside
Squares are the 8 years with analysed shifts, 2017 to 2026. A number is the questions that year when there is more than one; the shade is scaled to one shift, so a year with more analysed shifts (1 to 24 a year) does not look darker. Share is of the level above.
Ideas
Every idea inside this topic
9 different ideas were tested; 6 came more than once.
find unknown from infinite agp sum
Numerical value · 5 shifts · 3 numericalfind unknown from infinite series sum
Numerical value · 4 shifts · 2 numericalsum of series from recurrence
Single correct · 3 shifts · 1 numericalsum of finite arithmetico-geometric series
Numerical value · 3 shifts · 2 numericalagp terms from given sum
Numerical value · 2 shifts · 2 numericalfind constant and tail probability of discrete distribution
Single correct · 2 shiftssum of series with summation general term
Numerical value · 1 shift · 1 numericalsum of infinite power series in closed form
Single correct · 1 shiftevaluate infinite product via exponent series
Single correct · 1 shift
| Idea | Years asked | Times | Shifts | Format | Numerical |
|---|---|---|---|---|---|
| Sum of Infinite AGPfind unknown from infinite agp sum | 5 | 5 | Numerical valueCalculation | 3 | |
| Second-Order AGP Summationfind unknown from infinite series sum | 4 | 4 | Numerical valueMulti-step | 2 | |
| AGP Recurrence Relationsum of series from recurrence | 3 | 3 | Single correctMulti-step | 1 | |
| Sum of Finite AGPsum of finite arithmetico-geometric series | 3 | 3 | Numerical valueCalculation | 2 | |
| AGP General Termagp terms from given sum | 2 | 2 | Numerical valueMulti-step | 2 | |
| AGP in Expected Value Scenariosfind constant and tail probability of discrete distribution | 2 | 2 | Single correctCalculation | – | |
| Derivative Method for AGP Sumssum of series with summation general term | 1 | 1 | Numerical valueMulti-step | 1 | |
| Integration Method for Harmonic-Geometric Seriessum of infinite power series in closed form | 1 | 1 | Single correctMulti-step | – | |
| Infinite Product Reduction to AGPevaluate infinite product via exponent series | 1 | 1 | Single correctMulti-step | – |
Times and shifts count every analysed shift. Across JEE Main, 78% of questions since 2024 went back to an idea an earlier year had asked; the rest were new. All repeated ideas
Every question
Arithmetico-Geometric Series questions, year by year
The opening words of each question as it appeared in the official paper, with the idea it tested. Open one for its options and the official answer.
JEE Main 20251 question in 1 shift
- 3 Apr, Shift 2Q8If the probability that the random variable takes the value is given by , where…
Idea: Sum of Infinite AGP
Asked the year beforeMediumSingle correct
JEE Main 20242 questions in 2 shifts
- 6 Apr, Shift 1Q24Let the first term of a series be and its term , . If the sum of the…
Idea: AGP Recurrence Relation
HardNumerical value - 27 Jan, Shift 1Q24If , then the value of p is ________.
Idea: Sum of Infinite AGP
MediumNumerical value
JEE Main 20236 questions in 6 shifts
- 6 Apr, Shift 2Q23If , then is equal to ___________.
Idea: Sum of Finite AGP
Asked the year beforeHardNumerical value - 8 Apr, Shift 2Q17If the probability that the random variable takes values is given by , , where…
Idea: AGP in Expected Value Scenarios
MediumSingle correct - 10 Apr, Shift 2Q24Suppose be in an arithmetico-geometric progression. If the common ratio of the corresponding geometric progression…
Idea: AGP General Term
Asked the year beforeMediumNumerical value - 11 Apr, Shift 1Q25Let . Then the value of …
Idea: Sum of Finite AGP
Asked the year beforeMediumNumerical value - 11 Apr, Shift 2Q23For , if the sum of the series is ,…
Idea: Second-Order AGP Summation
Asked the year beforeHardNumerical value - 13 Apr, Shift 2Q25Let , . If then is equal to ______
Idea: Derivative Method for AGP Sums
New ideaHardNumerical value
JEE Main 20227 questions in 7 shifts
- 29 Jul, Shift 1Q24Let be an A.P. If , then is equal to __________.
Idea: Sum of Infinite AGP
Asked the year beforeMediumNumerical value - 29 Jul, Shift 2Q6Let be a sequence such that and . Then…
Idea: AGP Recurrence Relation
New ideaHardSingle correct - 25 Jun, Shift 2Q8The sum is equal to :
Idea: Sum of Finite AGP
New ideaEasySingle correct - 27 Jun, Shift 2Q5Let Then is equal to
Idea: Second-Order AGP Summation
Asked the year beforeMediumSingle correct - 29 Jun, Shift 1Q12Let be a sequence such that and for all . Then,…
Idea: AGP Recurrence Relation
New ideaMediumSingle correct - 29 Jun, Shift 2Q4The sum of the infinite series…
Idea: Second-Order AGP Summation
Asked the year beforeMediumSingle correct - 30 Jun, Shift 1Q22Let for , and . If are in an arithmatico-geometric progression, whose…
Idea: AGP General Term
New ideaMediumNumerical value
JEE Main 20215 questions in 5 shifts
- 27 Aug, Shift 1Q78If , then , is equal to :
Idea: Integration Method for Harmonic-Geometric Series
New ideaHardSingle correct - 31 Aug, Shift 2Q84If , then is equal to ______________.
Idea: Second-Order AGP Summation
New ideaHardNumerical value - 26 Feb, Shift 1Q78The sum of the infinite series is equal to :
Idea: Sum of Infinite AGP
New ideaEasySingle correct - 25 Jul, Shift 1Q84If the value of…
Idea: Sum of Infinite AGP
New ideaMediumNumerical value - 25 Jul, Shift 2Q70Let X be a random variable such that the probability function of a distribution is given by , …
Idea: AGP in Expected Value Scenarios
New ideaMediumSingle correct
JEE Main 20201 question in 1 shift
- 9 Jan, Shift 1Q57The product to is equal to :
Idea: Infinite Product Reduction to AGP
New ideaMediumSingle correct
Questions from the official JEE Main Paper 1 shifts published by NTA (CBSE for 2017). Questions NTA dropped are left out. Topic and idea tags, counts and notes are Lumi’s.