Arithmetic Progression (Missing Term)
Arithmetic Progression (AP) missing term problems present a sequence where one term is missing. You must find the missing term by identifying the common difference between consecutive terms.
What You'll Learn
Introduction to Arithmetic Progression (Missing Term)
Arithmetic Progression (AP) missing term problems present a sequence where one term is missing. You must find the missing term by identifying the common difference between consecutive terms.
Prerequisites
How to Solve Arithmetic Progression (Missing Term) Problems
Step 1: Identify two consecutive terms in the series (if available)
Step 2: Calculate the common difference: d = a₂ - a₁
Step 3: If the missing term is between known terms, use the AP formula
Step 4: If the missing term is at position n, use aₙ = a₁ + (n-1)d
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: 5, 9, 13, ?, 21 Solution: Step 1: Known terms: 5, 9, 13, _, 21 Step 2: Common difference d = 9 - 5 = 4 Step 3: Check: 13 + 4 = 17 Step 4: Check further: 17 + 4 = 21 ✓ Step 5: Missing term = 17 Answer: 17
Pro Tips & Tricks
- If missing term is between two known terms, it's the average of the two: a_missing = (a_left + a_right)/2
- For evenly spaced terms, the middle term is the arithmetic mean of its neighbors
- Common difference can be negative (decreasing sequence)
- Check if the sequence has a constant difference between ALL consecutive terms
- For larger gaps, use d = (a_last - a_first)/(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 Arithmetic Progression (Missing Term). Each worksheet contains 20 questions with detailed explanations. Start from Worksheet 1 and progress through increasing difficulty levels.
Exam Importance
Arithmetic Progression (Missing Term) is an important topic for various competitive exams. Here's how frequently it appears:
Ready to Master Arithmetic Progression (Missing Term)?
Start with Worksheet 1 and work your way up to expert level! Each worksheet includes: