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Chapter 12: Q.81 (page 825)

Find x so that x, x + 2, and x + 3 are consecutive terms of a geometric sequence.

Short Answer

Expert verified

The value of x is - 4.

Step by step solution

01

Step 1. Given information

Given terms are x, x + 2, and x + 3 are consecutive terms of a

geometric sequence.

02

Step 2. Equation for geometric sequence.

The common ratio of geometric sequence is $\frac{a_{1}}{a_{2}} = \frac{a_{2}}{a_{3}}$

Where $a_{1}$ , $a_{2}$ and $a_{3}$ are the consecutive terms of Geometric sequence. So, The terms are in common ratio.

$\frac{x}{x + 2} = \frac{x + 2}{x + 3}$

${(x + 2)}^{2} = x (x + 3)$

03

Step 3. Solving the Geometric Proportional ratio equation .

Solving the equation :

${(x + 2)}^{2} = x (x + 3) x^{2} + 4 x + 4 = x^{2} + 3 x x^{2} + 4 x + 4 - 4 = x^{2} + 3 x - 4 x^{2} + 4 x = x^{2} + 3 x - 4 x^{2} + 4 x - (x^{2} + 3 x) = x^{2} + 3 x - 4 - (x^{2} + 3 x) x = - 4$

Therefore, the value of x is -4 .

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Most popular questions from this chapter

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