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.
What You'll Learn
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
How to Solve GP Missing Term Problems
Step 1: Identify two consecutive terms in the series (if available)
Step 2: Calculate the common ratio: r = a₂/a₁
Step 3: If the missing term is between known terms, use the GP formula
Step 4: If the missing term is at position n, use aₙ = a₁ × r^(n-1)
Step 5: Calculate the missing term
Step 6: Verify by checking if the term fits the sequence
Step 7: Present the missing term
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
Common Mistakes to Avoid
Practice Worksheets
Practice makes perfect! Work through these worksheets to master GP Missing Term. Each worksheet contains 20 questions with detailed explanations. Start from Worksheet 1 and progress through increasing difficulty levels.
Exam Importance
GP Missing Term is an important topic for various competitive exams. Here's how frequently it appears:
Ready to Master GP Missing Term?
Start with Worksheet 1 and work your way up to expert level! Each worksheet includes: