If x, 2x + 2,and 3x + 3 are in a geometric pr | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) Given that $x, 2x + 2$,and $3x + 3$ are in a geometric progression $(GP)$.For a $GP$,the square of the middle term is equal to the product of the

Vedclass · Accepted Answer

$-13.5$

Vedclass · Answer

(D) Given that $x, 2x + 2$,and $3x + 3$ are in a geometric progression $(GP)$.For a $GP$,the square of the middle term is equal to the product of the first and third terms: $(2x + 2)^2 = x(3x + 3)$.Expanding this,we get $4x^2 + 8x + 4 = 3x^2 + 3x$.Rearranging the terms gives the quadratic equation $x^2 + 5x + 4 = 0$.Factoring the equation,we get $(x + 1)(x + 4) = 0$,which gives $x = -1$ or $x = -4$.If $x = -1$,the terms are $-1, 0, 0$,which cannot form a $GP$.If $x = -4$,the terms are $-4, -6, -9$. The common ratio $r = \frac{-6}{-4} = 1.5$.The fourth term $t_4 = a 	imes r^3 = -4 	imes (1.5)^3$.$t_4 = -4 	imes 3.375 = -13.5$.

If $x, 2x + 2$,and $3x + 3$ are in a geometric progression,what is the fourth term?

Similar Questions

Find the fractional value of $0.125125125 \dots$

What will $Rs. 500$ amount to in $10$ years after its deposit in a bank which pays an annual interest rate of $10\%$ compounded annually?

Let $a_{n}$ be the $n^{\text{th}}$ term of a $G$.$P$. of positive terms. If $\sum_{n=1}^{100} a_{2n+1} = 200$ and $\sum_{n=1}^{100} a_{2n} = 100$,then $\sum_{n=1}^{200} a_{n}$ is equal to:

The roots of the equation $x^3-14x^2+56x-64=0$ are in

Show that the ratio of the sum of the first $n$ terms of a $G.P.$ to the sum of the terms from the $(n+1)^{th}$ to the $(2n)^{th}$ term is $\frac{1}{r^{n}}$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module