GP Missing Term

Geometric Progression (GP) missing term problems present a sequence where one term is missing. You must find the missing term by identifying the common ratio between consecutive terms.

10Worksheets
200+Practice Questions
IntermediateDifficulty
2-3 hoursHours to Master

Introduction to GP Missing Term

Geometric Progression (GP) missing term problems present a sequence where one term is missing. You must find the missing term by identifying the common ratio between consecutive terms.

Prerequisites

Geometric Progression concept Common ratio formula: r = a₂/a₁ nth term formula: aₙ = a₁ × r^(n-1) Basic arithmetic
Why This Matters: GP missing term problems appear in 1-2 questions in SSC CGL and Banking PO exams. They test understanding of geometric sequences.

How to Solve GP Missing Term Problems

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Step 1: Identify two consecutive terms in the series (if available)

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

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Step 3: If the missing term is between known terms, use the GP formula

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Step 4: If the missing term is at position n, use aₙ = a₁ × r^(n-1)

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Step 5: Calculate the missing term

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Step 6: Verify by checking if the term fits the sequence

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Step 7: Present the missing term

Pro Strategy: Always find the common ratio first. If consecutive terms are not available, use any two known terms to find r = (a_m/a_n)^(1/(m-n)).

Example Problem

Example: Find the missing term: 2, 6, 18, ?, 162 Solution: Step 1: Known terms: 2, 6, 18, _, 162 Step 2: Common ratio r = 6/2 = 3 Step 3: Check: 18 × 3 = 54 Step 4: Check further: 54 × 3 = 162 ✓ Step 5: Missing term = 54 Answer: 54

Pro Tips & Tricks

  • If missing term is between two known terms, it's the geometric mean: a_missing = √(a_left × a_right)
  • For evenly spaced terms, the middle term is the geometric mean of its neighbors
  • Common ratio can be fractional (decreasing sequence) or negative (alternating signs)
  • Check if the sequence has a constant ratio between ALL consecutive terms
  • For larger gaps, use r = (a_last/a_first)^(1/(n-1))
  • Always verify your answer by checking the sequence

Shortcut Methods to Solve Faster

Middle term = √(First × Last) for three-term GP
aₙ = a₁ × r^(n-1)
r = (a_m/a_n)^(1/(m-n))

Common Mistakes to Avoid

Using ratio as difference (confusing AP with GP)
Assuming r > 1 when it could be fractional
Not verifying the pattern with all given terms
Forgetting that r can be negative

Exam Importance

GP Missing Term 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 GP Missing Term?

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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