JEE Main Maths · Sequences and Series

Arithmetico-Geometric Series in JEE Main

Name: Arithmetico-Geometric Series: JEE Main previous year questions
Creator: Lumi

Arithmetico-Geometric Series (Maths, Sequences and Series) came 6 times in 6 of the 42 JEE Main shifts Lumi analysed, across 5 distinct ideas. 1 of them came in 2024–26; it was last asked in 2025.

Questions: 6; in 6 shifts
Ideas asked: 5; 1 asked more than once
Numerical answer: 3; 50% of its questions
Pattern: Comes in cycles; last asked 2025

Questions each year

In the shifts Lumi analysed for each year.

Difficulty and format

Easy 0Medium 5Hard 1

Format

Single correct3 Q
Numerical value3 Q

Ideas inside the topic

5 ideas

Sum of Infinite AGP2 Q
Derivative Method for AGP Sums1 Q
AGP in Expected Value Scenarios1 Q
AGP Recurrence Relation1 Q
Sum of Finite AGP1 Q

Where it sits

Part of Sequences and Series, which had 73 questions in all. Arithmetico-Geometric Series accounts for 8% of them. In Lumi's JEE taxonomy it belongs to Algebra.

Some questions sit in other chapters too: Limits and Derivatives, Probability.

Every question

All 6 Arithmetico-Geometric Series questions

Newest first, each with its options and official answer.

3 Apr 2025, Shift 2 · Q8If the probability that the random variable $X$ takes the value $x$ is given by $P(X = x) = k(x + 1)3^{-x},\ x = 0, 1, 2, 3\ldots$ , where…MediumSingle correct
8 Apr 2023, Shift 2 · Q17If the probability that the random variable $X$ takes values $x$ is given by $P(X = x) = k(x + 1)3^{-x}$ , $x = 0, 1, 2, 3, \ldots$ , where…MediumSingle correct
11 Apr 2023, Shift 1 · Q25Let $S = 109 + \frac{108}{5} + \frac{107}{5^2} + \ldots + \frac{2}{5^{107}} + \frac{1}{5^{108}}$ . Then the value of $(16S - (25)^{-54})$ …MediumNumerical value
13 Apr 2023, Shift 2 · Q25Let $f(x)=\sum_{k=1}^{10}k\,x^k$ , $x\in\mathbb{R}$ . If $2f(2)+f'(2)=119(2)^n+1$ then $n$ is equal to ______HardNumerical value
29 Jun 2022, Shift 1 · Q12Let $\{a_n\}_{n=0}^{\infty}$ be a sequence such that $a_0 = a_1 = 0$ and $a_{n+2} = 2a_{n+1} - a_n + 1$ for all $n \ge 0$ . Then,…MediumSingle correct
25 Jul 2021, Shift 1 · Q84If the value of…MediumNumerical value