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The second, Forth and Sixth terms of a Geometric Progression (G.P.) are (2x-4), (13x+4 and (122x-4) Deatree, Find the (1) Value of x (1) Common ratio Cui) First term

The second, Forth and Sixth terms of a Geometric Progression (G.P.) are (2x-4), (13x+4 and (122x-4) Deatree, Find the (1) Value of x (1) Common ratio Cui) First term

Algebra and Trigonometry (6th Edition)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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### Geometric Progression Problem The second, fourth, and sixth terms of a Geometric Progression (G.P) are \( (2x - 4) \), \( (18x + 4) \), and \( (162x - 4) \) respectively. Find the: (i) **Value of \( x \)** (ii) **Common ratio** (iii) **First term** #### Solution Approach: 1. **Identify the terms:** - Second term = \( 2x - 4 \) - Fourth term = \( 18x + 4 \) - Sixth term = \( 162x - 4 \) 2. **Set up the equations for a G.P:** The general form for the terms of a G.P. can be written as follows: - Second term = \( ar \) - Fourth term = \( ar^3 \) - Sixth term = \( ar^5 \) 3. **Solve for \( x \), the common ratio \( r \), and the first term \( a \):** By comparing \((2x - 4)\), \((18x + 4)\) and \((162x - 4)\) with the terms \(ar\), \(ar^3\), and \(ar^5\) respectively, you can create a system of equations to solve for \( x \). #### Resources To solve this problem, you may need to understand the following concepts: - Properties of Geometric Progressions. - Algebraic manipulation and solving systems of equations. #### Additional Information For a deeper understanding and further examples of Geometric Progressions, please refer to our section on sequences and series.
Transcribed Image Text:### Geometric Progression Problem The second, fourth, and sixth terms of a Geometric Progression (G.P) are \( (2x - 4) \), \( (18x + 4) \), and \( (162x - 4) \) respectively. Find the: (i) **Value of \( x \)** (ii) **Common ratio** (iii) **First term** #### Solution Approach: 1. **Identify the terms:** - Second term = \( 2x - 4 \) - Fourth term = \( 18x + 4 \) - Sixth term = \( 162x - 4 \) 2. **Set up the equations for a G.P:** The general form for the terms of a G.P. can be written as follows: - Second term = \( ar \) - Fourth term = \( ar^3 \) - Sixth term = \( ar^5 \) 3. **Solve for \( x \), the common ratio \( r \), and the first term \( a \):** By comparing \((2x - 4)\), \((18x + 4)\) and \((162x - 4)\) with the terms \(ar\), \(ar^3\), and \(ar^5\) respectively, you can create a system of equations to solve for \( x \). #### Resources To solve this problem, you may need to understand the following concepts: - Properties of Geometric Progressions. - Algebraic manipulation and solving systems of equations. #### Additional Information For a deeper understanding and further examples of Geometric Progressions, please refer to our section on sequences and series.
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