JEE Main Maths · Sequences & Series PYQ

JEE Main Sequences & Series Previous Year Questions (2002–2025)

Sequences & Series is a P1 Algebra chapter — ~5% JEE Main weightage with 1–2 questions per session. AP, GP, HP, AGP and AM-GM-HM inequality questions appear regularly. Mastery here accelerates Binomial Theorem and Probability downstream.

Sequences & Series PYQs from 2002 to 2025, tagged by sub-topic (AP, GP, telescopic, inequality) and difficulty. Every solution identifies the sequence type and applies the correct formula.

Practise Sequences & Series PYQs All Maths PYQs

Sequences & Series at a Glance

Weightage

~5%

approx · 10-yr avg

Priority

Must master

Year range

2002–2025

PYQ coverage

Typical in paper

1–2

per session

Key Sub-Topics & What's Tested

Arithmetic Progression (AP)

nth term a_n = a + (n-1)d, sum S_n = n/2 [2a + (n-1)d] = n/2 (a + l), properties, insertion of AMs.

Geometric Progression (GP)

nth term a_n = ar^(n-1), sum S_n = a(r^n - 1)/(r-1), infinite GP S_∞ = a/(1-r) for |r| < 1, insertion of GMs.

Harmonic Progression (HP)

Sequence whose reciprocals are in AP, harmonic mean, relationship with AP via reciprocal transformation.

AGP (Arithmetic-Geometric)

Terms of form (a + (n-1)d)·r^(n-1), sum formulas, applications in derivative of GP series.

AM ≥ GM ≥ HM Inequality

For positive reals, AM ≥ GM ≥ HM with equality iff all equal, weighted versions, applications in optimisation.

Sum of Special Series

Σn = n(n+1)/2, Σn² = n(n+1)(2n+1)/6, Σn³ = [n(n+1)/2]², sum of cubes, telescopic series techniques.

Telescopic Series

Series of form Σ[f(k+1) - f(k)] collapse to f(n+1) - f(1); partial fractions decomposition often unlocks telescopic form.

Insertion of Means

Inserting k AMs between a and b, k GMs between a and b, relationship A·H = G² for single means.

Question Type Distribution

Question Type	Share (approx)	Example Pattern
AP nth Term / Sum	20%	Given AP with sum of first 10 terms = 100, find 5th term.
GP nth Term / Sum	20%	Sum of infinite GP = 3, first term = 2 — find common ratio.
AM-GM Inequality	15%	Find minimum value of x + 1/x for x > 0 using AM-GM.
AGP Sum	10%	Sum to infinity of 1 + 2x + 3x² + 4x³ + ... for \|x\| < 1.
Telescopic Series	15%	Evaluate Σ 1/[k(k+1)] for k from 1 to n.
Mixed / Insertion	20%	Four GMs between 2 and 54 — find the second GM.

How to Solve Sequences & Series PYQs

1
Identify the sequence type first. AP (constant difference), GP (constant ratio), HP (AP of reciprocals), AGP (AP × GP). Wrong identification breaks everything.
2
For sum problems, use standard formulas. S_n = n/2(a + l) for AP; S_n = a(r^n - 1)/(r-1) for GP. Memorise, don't re-derive every time.
3
AM-GM for optimisation: set up the inequality. Arithmetic Mean ≥ Geometric Mean with equality at AM = GM. Use for finding min/max of products and sums.
4
Telescopic series: partial fractions. For Σ 1/[k(k+a)], decompose as (1/a)[1/k - 1/(k+a)] to unlock telescopic collapse.
5
For infinite GP, check |r| < 1. S_∞ exists only if |r| < 1. If r ≥ 1, series diverges — don't apply S_∞ formula.

Common Mistakes That Cost Marks

Using AM instead of HM for harmonic problems. Average speed over equal distances = HM of speeds, NOT AM. Classic trap.
Forgetting (n-1) in nth term formula. a_n = a + (n-1)d, NOT a + nd. Off-by-one error is the #1 AP mistake.
Applying AM-GM with negative terms. AM-GM works only for non-negative reals. If any term can be negative, split cases.
Wrong infinite GP condition. Formula works only for |r| < 1. If r = 1 or r > 1, sum diverges.
Miscounting AMs/GMs inserted. If k AMs are inserted between a and b, total sequence has k+2 terms (a, k AMs, b). Common off-by-one in insertion problems.

JEE Main Maths PYQ Chapter-Wise

Browse PYQs across all Maths chapters.

JEE Main Matrices & Determinants PYQ

P1 Algebra chapter — companion topic.

JEE Main Probability PYQ

Uses series sums for expected value computations.

Top High-Weightage Maths Chapters (data-backed)

Where Sequences & Series sits in the priority order.

JEE Main Maths Syllabus with Priority Tiers

Full Maths syllabus with priority tiers.

JEE Main Rank Predictor

Convert a target percentile into an expected rank.

Frequently asked questions

How many Sequences & Series PYQs should I solve?

Target 60–80 PYQs across 2010–2025. Given high template repeat (AP/GP sum, AM-GM) and 5% weightage, focused practice locks in reliable scores.

Is AGP heavily tested in JEE Main?

Moderately — 2-3 AGP PYQs per 10-year window. Usually as sum to infinity of an AGP with simple coefficients. Master the differentiation trick: AGP sum = differentiate GP.

Do I need to memorise sum formulas?

Yes — Σn, Σn², Σn³ formulas and AP/GP sum formulas are non-negotiable. Saves 90+ seconds per question vs deriving from scratch.

What's the most useful AM-GM application?

Finding minimum of a + b when ab = constant (or vice versa). PYQs wrap this in word problems — identify the constraint, apply AM ≥ GM.

How do I spot telescopic series?

Look for Σ of fractions like 1/[k(k+1)] or Σ of differences f(k+1) - f(k). If you can partial-fraction or recognize telescopic pattern, series collapses cleanly.

Does Sequences & Series connect with other chapters?

Yes — Binomial Theorem (sum of coefficients), Probability (expected value computations), Integration (Riemann sums). Strong fluency here helps downstream.

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