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9.Geometric Progression (GP)
Class 11 • Mathematics • NCERT
Geometric Progression (GP)
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This lesson introduces Geometric Progressions as per NCERT Class 11. Students learn the definition of a GP, identify the first term and common ratio, and find the general term using simple, exam-oriented examples.
Lesson Objectives
- Understand what a Geometric Progression is.
- Identify the first term and common ratio.
- Find the nth term of a GP.
- Solve basic NCERT-style problems.
1. What Is a Geometric Progression?
A Geometric Progression (GP) is a sequence in which each term after the first is obtained by multiplying the previous term by a fixed non-zero number.
Examples of GPs:
• 2, 4, 8, 16, …
• 81, 27, 9, 3, …
• 2, 4, 8, 16, …
• 81, 27, 9, 3, …
2. First Term and Common Ratio
In a GP:
• First term = a
• Common ratio = r = (second term) ÷ (first term)
• Common ratio = r = (second term) ÷ (first term)
3. General Term of a GP
The nth term (general term) of a GP is given by:
Tn = arn−1
4. Simple NCERT Examples
• Find the 5th term of GP: 3, 6, 12, …
Here, a = 3, r = 2
T5 = 3 × 2⁴ = 48
Here, a = 3, r = 2
T5 = 3 × 2⁴ = 48
5. Important NCERT Notes
• Common ratio can be positive, negative, or fractional
• GP with r = 1 is a constant sequence
• r cannot be zero
• GP with r = 1 is a constant sequence
• r cannot be zero
Practice Questions (NCERT)
- Define a Geometric Progression.
- Find the common ratio of GP: 5, 10, 20, …
- Find the first term of GP: 16, 8, 4, …
- Write the formula for the nth term of a GP.
- Find the 6th term of GP: 2, 6, 18, …
- Can the common ratio be a fraction?
- What happens if r = 1?
- Can r be zero?
- Is 3, −6, 12, −24, … a GP?
- Is this topic part of NCERT Class 11 syllabus?
✅ Show Answer Key
- A sequence with constant ratio between consecutive terms.
- 2
- 16
- Tn = arn−1
- 162
- Yes
- Sequence becomes constant.
- No
- Yes
- Yes
© Aviate Learning – Sequences & Series (NCERT Class 11)