Overview of Progressions in JEE Maths

Progressions are one of the most scoring topics in JEE Maths. They allow students to analyze sequences of numbers with patterns and solve problems using formulas and shortcuts. At StudentBro.in, we provide a complete guide covering Arithmetic Progression (AP), Geometric Progression (GP), and Harmonic Progression (HP) with step-by-step explanations, formulas, examples, and practice questions to help JEE aspirants excel.

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What is a Progression?

A progression is a sequence of numbers arranged according to a specific rule or pattern.

• Arithmetic Progression (AP): A sequence in which the difference between consecutive terms is constant.

• Geometric Progression (GP): A sequence in which the ratio of consecutive terms is constant.

• Harmonic Progression (HP): A sequence in which the reciprocals of the terms form an arithmetic progression.

Example:

• AP: 2, 5, 8, 11 (common difference = 3)

• GP: 3, 6, 12, 24 (common ratio = 2)

• HP: 1, 1/3, 1/5, 1/7 (reciprocals form an AP)

Arithmetic Progression (AP)

Definition: A sequence where the difference between consecutive terms is constant (d).

General Term (nth term):
Tₙ = a + (n - 1)d

Sum of n Terms:
Sₙ = n/2 [2a + (n - 1)d] = n/2 (a + l)

Where:

• a = first term

• d = common difference

• l = last term

• n = number of terms

Applications in JEE:

• Finding nth term of sequences

• Sum of numbers in series

• Solving word problems involving age, salary, or distances

Example: Find the 10th term of AP: 2, 5, 8, …
T₁₀ = 2 + (10-1)*3 = 29

Geometric Progression (GP)

Definition: A sequence where each term after the first is obtained by multiplying the previous term by a constant (r).

General Term (nth term):
Tₙ = a * r^(n-1)

Sum of n Terms:
Sₙ = a (rⁿ - 1) / (r - 1), r ≠ 1

Sum to Infinity (|r| < 1):
S∞ = a / (1 - r)

Applications in JEE:

• Compound interest problems

• Population growth and decay

• Series sum problems in advanced questions

Example: GP: 2, 6, 18, …; 5th term = 2 * 3⁴ = 162

Harmonic Progression (HP)

Definition: A sequence in which reciprocals of the terms form an arithmetic progression.

• HP term: If 1/T₁, 1/T₂, … form an AP, then the sequence is HP.

Relation to AP:

• Convert HP to AP using reciprocals

• Solve sum and term problems using AP formulas

Example: 1, 1/3, 1/5, … → reciprocals 1, 3, 5 form an AP

Important Formulas for Progressions

AP Formulas:

• Tₙ = a + (n-1)d

• Sₙ = n/2 [2a + (n-1)d]

GP Formulas:

• Tₙ = a * r^(n-1)

• Sₙ = a(rⁿ - 1)/(r - 1), r ≠ 1

• S∞ = a / (1 - r), |r| < 1

HP Formulas:

• Convert to AP: 1/Tₙ = a + (n-1)d

• Sum and nth term derived using AP relations

Tips and Tricks for JEE Progressions

1. Memorize AP, GP, HP formulas thoroughly

2. Practice nth term and sum problems daily

3. Convert HP to AP to simplify problems

4. Learn shortcuts for sum of series questions

5. Solve previous year JEE progression problems for speed

Applications of Progressions in JEE Exams

• AP: Age-related, salary, distance, or time problems

• GP: Compound interest, population growth, decay problems

• HP: Series involving reciprocals in physics or math word problems

• Many mixed progression problems combine AP, GP, and HP

Example: A train covers distances in AP: 10, 15, 20 … Find distance covered in 12th interval.

StudentBro.in JEE Maths Progression Section

At StudentBro.in, students can access:

• Step-by-step explanations of AP, GP, HP formulas

• Worked examples for each type of progression

• Practice problems with solutions and shortcuts

• Tips for quick calculation and exam strategy

• Revision notes for last-minute preparation

Practice Questions and Sample Problems

1. Find the 20th term of AP: 3, 7, 11, …

2. Sum of first 15 terms of AP: 5, 8, 11, …

3. Find the 6th term of GP: 2, 4, 8, …

4. Sum to infinity of GP: 3, 3/2, 3/4, …

5. Find 4th term of HP: 1, 1/3, 1/5, …

Regular practice improves accuracy, speed, and confidence in solving progression problems.

Conclusion

Progressions are a high-scoring chapter in JEE Maths. Understanding AP, GP, and HP formulas, combined with practice, allows students to solve problems quickly and accurately. At StudentBro.in, we provide a complete guide from basics to advanced problem-solving, making progressions simple and exam-oriented.

Mastering progressions ensures students can tackle numerical and series problems confidently in both JEE Main and Advanced exams.