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Geometric Progression

Geometric Progression (GP) problems present sequences where each term is obtained by multiplying the previous term by a fixed constant called the common ratio. These problems test your ability to identify multiplicative patterns and extend sequences using the formula aₙ = a₁ × r^(n-1).

10Worksheets
200+Practice Questions
BeginnerDifficulty
1-2 hoursHours to Master

What You'll Learn

Introduction & Overview Why This Matters How to Solve Pro Tips & Tricks
Shortcut Methods Common Mistakes Practice Worksheets Exam Importance

Introduction to Geometric Progression

Geometric Progression (GP) problems present sequences where each term is obtained by multiplying the previous term by a fixed constant called the common ratio. These problems test your ability to identify multiplicative patterns and extend sequences using the formula aₙ = a₁ × r^(n-1).

Prerequisites

Basic multiplication and division Understanding of constant ratio Exponent concepts nth term formula
Why This Matters: Geometric Progression problems appear in 1-2 questions in SSC CGL and Banking PO exams. They test understanding of multiplicative patterns.

How to Solve Geometric Progression Problems

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Step 1: Identify the first term (a) and second term of the sequence

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Step 2: Calculate the common ratio: r = a₂ ÷ a₁

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Step 3: Verify the ratio is constant for all consecutive terms

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Step 4: For next term: multiply the last term by r

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Step 5: For missing term: use aₙ = a₁ × r^(n-1)

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Step 6: For wrong term identification: find where the ratio breaks pattern

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Step 7: Verify your answer by checking consistency with the sequence

Pro Strategy: Always calculate the common ratio first by dividing any term by its previous term. The ratio must be constant throughout the sequence. For fractional ratios, the sequence may be decreasing.

Example Problem

Example: Find the next term in the sequence: 3, 6, 12, 24, ___ Solution: Step 1: First term a = 3, second term = 6 Step 2: Common ratio r = 6 ÷ 3 = 2 Step 3: Check: 12÷6=2, 24÷12=2 ✓ Step 4: Next term = 24 × 2 = 48 Answer: 48

Pro Tips & Tricks

  • Common ratio r = a₂ ÷ a₁ = a₃ ÷ a₂
  • nth term formula: aₙ = a₁ × r^(n-1)
  • If |r| < 1, the sequence decreases toward zero
  • If r is negative, the terms alternate signs
  • Three terms in GP can be written as a/r, a, ar
  • The geometric mean of a and b is √(a×b)

Shortcut Methods to Solve Faster

Next term = Last term × Common ratio
Missing term = √(First × Last) for three-term GP
r = (aₘ ÷ aₙ)^(1/(m-n))
For alternating signs, r is negative

Common Mistakes to Avoid

Using addition instead of multiplication
Forgetting that ratio can be fractional
Confusing GP with arithmetic progression
Not handling negative ratios correctly

Exam Importance

Geometric Progression is an important topic for various competitive exams. Here's how frequently it appears:

SSC CGL
1-2 questions
BANKING PO
1-2 questions
RAILWAYS RRB
1-2 questions
CAT
1-2 questions
INSURANCE
1-2 questions

Ready to Master Geometric Progression?

Start with Worksheet 1 and work your way up to expert level! Each worksheet includes:

20 practice questions
Detailed solutions
Step-by-step explanations
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