If a², b², c² Are in A.P. — Find Relation Between a, b, c
Understanding the condition when a² b² c² in arithmetic progression is a common algebra problem in higher-secondary mathematics. Here we derive the required relationship between a, b, and c.
Given
a², b², c² are in A.P. (Arithmetic Progression)
Condition for Terms in A.P.
If three terms are in A.P., then twice the middle term = sum of the first and third terms.
⇒ 2b² = a² + c²
Deriving the Relation
From 2b² = a² + c², rearrange to find the relationship between a, b and c:
a² − 2b² + c² = 0
⇒ (a − b)(a + b) + (c − b)(c + b) = 0
This simplifies to the identity:
(a − b)(a + b) = −(c − b)(c + b)
The main requirement for arithmetic progression of squares is the equality of 2b² with the sum of the squares of the other two terms.
If a², b², c² Are in A.P. — Find Relation Between a, b, c
Keywords
a² b² c² in arithmetic progression, arithmetic progression relation, algebra problem, mean of squares, quadratic relation, Class 11 math, Class 12 math, exam preparation, algebra notes, a, b, c relation, sequence and series
Tags
arithmetic progression, algebra, sequence and series, Class 11, Class 12, math notes, a² b² c², relation problems, exam question, aklearningnepal, education,If a², b², c² Are in A.P. — Find Relation Between a, b, c
📘 Latest Related Questions
- Class 12 NEB Account Set A Solution 2083 |
- NEB Model Question (Set A) Accounting Question 22 Solution | The opening and closing balance of inventories are as below:
- NEB Model Question (Set A) Accounting Question 21 Solution | The Balance Sheet of a company on 31st December were given below:
- NEB Model Question (Set A) Accounting Question 20 Solution | The following Trial Balance of a company as on 31st Chaitra last year is given below:
- NEB Model Question (Set A) Accounting Question 19 Solution | Explain the features of accounting software.
- NEB Model Question (Set A) Accounting Question 18 Solution | The time allowed to produce 80 units of output is 2 hours. A worker produced 400 units during the month. Wages rate per hour is Rs. 800. Find the wages of the worker.
- NEB Model Question (Set A) Accounting Question 17 Solution | State the meaning of material classification with suitable examples.
- NEB Model Question (Set A) Accounting Question 15 Solution | The Trial Balance of a Company Ltd. as on 31st Chaitra last year is given below:
- NEB Model Question (Set A) Accounting Question 16 Solution | Differentiate between cost accounting and financial accounting.
- NEB Model Question (Set A) Accounting Question 14 Solution | Following information was taken from a company as on 31st Ashad, last year:
- NEB Model Question (Set A) Accounting Question 12 Solution | A Company Ltd. invited applications for 30,000 shares of Rs. 100 each at 10% premium. Payment: Application Rs. 30, Allotment Rs. 40, First & Final Call Rs. 40. Received 42,000 applications. Allotment: 25,000 full, 10,000 50%, 7,000 rejected. Excess money adjusted with allotment. Call money on 200 shares not received.
- NEB Model Question (Set A) Accounting Question 13 Solution | A company purchased the following assets at an agreed price of Rs. 1,100,000: Plant Rs. 520,000, Land and Building Rs. 730,000. The company paid the agreed price by issuing shares of Rs. 100 each at 20% discount. Required: Entries for purchase of assets and issue of shares.
- NEB
- Class 12 Old Is Gold 2083 App
- Class 11 Old Is Gold 2083 App
- Class 12 Nepali Old is Gold Set 1 Solution 2083 | NEB Exam Guide
- Class 10 OCE Social Studies Model Question Solution | SEE Social Studies 1 Sets Model Question Solution 2082
- Class 10 OCE Science Model Question Solution | SEE Science 3 Sets Model Question Solution2082
- Class 10 OCE Math Model Question Solution | SEE Math 3 Sets Model Question Solution
- mm
If a², b², c² Are in A.P. — Find Relation Between a, b, c
