HP Missing Term
Harmonic Progression (HP) missing term problems present a sequence of numbers whose reciprocals form an arithmetic progression. You must find the missing term by converting to AP, finding the missing reciprocal, then converting back.
What You'll Learn
Introduction to HP Missing Term
Harmonic Progression (HP) missing term problems present a sequence of numbers whose reciprocals form an arithmetic progression. You must find the missing term by converting to AP, finding the missing reciprocal, then converting back.
Prerequisites
How to Solve HP Missing Term Problems
Step 1: Take reciprocals of all given HP terms to get an AP
Step 2: Find the missing term in this AP using AP methods
Step 3: Take the reciprocal of the AP missing term
Step 4: This reciprocal is the missing HP term
Step 5: Verify by checking the original HP sequence
Step 6: Present the missing HP term
Example Problem
Example: Find the missing term in HP: 1/2, 1/5, 1/8, ?, 1/14 Solution: Step 1: Reciprocals: 2, 5, 8, _, 14 (this is an AP) Step 2: AP common difference d = 5-2 = 3 Step 3: Next term: 8 + 3 = 11 Step 4: Check: 11 + 3 = 14 ✓ Step 5: Missing HP term = 1/11 Answer: 1/11
Pro Tips & Tricks
- HP of the form: 1/a, 1/(a+d), 1/(a+2d), ...
- Three terms in HP: a, b, c satisfy 2/b = 1/a + 1/c
- The harmonic mean of a and c is 2ac/(a+c)
- If a, b, c are in HP, then 1/a, 1/b, 1/c are in AP
- Always check if terms are positive (HP usually defined for positive numbers)
- For fractions, take reciprocal carefully
Shortcut Methods to Solve Faster
Common Mistakes to Avoid
Practice Worksheets
Practice makes perfect! Work through these worksheets to master HP Missing Term. Each worksheet contains 20 questions with detailed explanations. Start from Worksheet 1 and progress through increasing difficulty levels.
Exam Importance
HP Missing Term is an important topic for various competitive exams. Here's how frequently it appears:
Ready to Master HP Missing Term?
Start with Worksheet 1 and work your way up to expert level! Each worksheet includes: