The terms of a G.P. are positive. If each ter | vedclass

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Question

(a) Under condition ${T_n} = {T_{n + 1}} + {T_{n + 2}}$

$ \Rightarrow a{r^{n - 1}} = a{r^n} + a{r^{n + 1}} $

$\Rightarrow {r^{n - 1}} = {r^n}(1

Vedclass · Accepted Answer

$\frac{{\sqrt 5 - 1}}{2}$

Vedclass · Answer

(a) Under condition ${T_n} = {T_{n + 1}} + {T_{n + 2}}$

$ \Rightarrow a{r^{n - 1}} = a{r^n} + a{r^{n + 1}} $

$\Rightarrow {r^{n - 1}} = {r^n}(1 + r)$

$ \Rightarrow $ ${r^2} + r - 1 = 0$

$ \Rightarrow r = \frac{{ - 1 \pm \sqrt {1 + 4} }}{2} = \frac{{ - 1 \pm \sqrt 5 }}{2}$

Since, each term is $ + ve$.

Hence common ratio is $\frac{{\sqrt 5 - 1}}{2}$.

The terms of a $G.P.$ are positive. If each term is equal to the sum of two terms that follow it, then the common ratio is

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