If the 4^{th}, 7^{th} and 10^{th} terms of a | vedclass

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

Question

(C) Let the first term of the $G.P.$ be $A$ and the common ratio be $r$.We know that the $n^{th}$ term of a $G.P.$ is given by $T_n = A r^{n-1}$.Given

Vedclass · Accepted Answer

$b^2 = ac$

Vedclass · Answer

(C) Let the first term of the $G.P.$ be $A$ and the common ratio be $r$.We know that the $n^{th}$ term of a $G.P.$ is given by $T_n = A r^{n-1}$.Given terms are:$T_4 = a = A r^3$$T_7 = b = A r^6$$T_{10} = c = A r^9$Now,consider the product $ac$:$ac = (A r^3) 	imes (A r^9) = A^2 r^{12}$Also,consider $b^2$:$b^2 = (A r^6)^2 = A^2 r^{12}$Since $b^2 = A^2 r^{12}$ and $ac = A^2 r^{12}$,it follows that $b^2 = ac$.Therefore,$a, b, c$ are in $G.P.$

If the $4^{th}, 7^{th}$ and $10^{th}$ terms of a $G.P.$ are $a, b, c$ respectively,then the relation between $a, b, c$ is

Similar Questions

If $2^{10} + 2^{9} \cdot 3^{1} + 2^{8} \cdot 3^{2} + \ldots + 2^{0} \cdot 3^{10} = S - 2^{11}$,then $S$ is equal to

If $\log 2, \log (2^n - 1)$ and $\log (2^n + 3)$ are in $A.P.$,then $n =$

The fifth term of the $H.P.$,$2, 2\frac{1}{2}, 3\frac{1}{3}, \dots$ will be

If $1 + \sin x + \sin^2 x + \dots \infty = 4 + 2\sqrt{3}$,where $0 < x < \pi$,then:

The sum of the series $1 + \frac{1}{1 + 2} + \frac{1}{1 + 2 + 3} + \dots$ up to $10$ terms is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module