If every term of a G.P. with positive terms i | vedclass

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Question

(d) Let first term and common ratio of $G.P.$ are respectively $a$ and $r$,

then under condition,

${T_n} = {T_{n - 1}} + {T_{n - 2}}$

$ \Righ

Vedclass · Accepted Answer

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

Vedclass · Answer

(d) Let first term and common ratio of $G.P.$ are respectively $a$ and $r$,

then under condition,

${T_n} = {T_{n - 1}} + {T_{n - 2}}$

$ \Rightarrow $ $a{r^{n - 1}} = a{r^{n - 2}} + a{r^{n - 3}}$

$ \Rightarrow $ $a{r^{n - 1}} = a{r^{n - 1}}{r^{ - 1}} + a{r^{n - 1}}{r^{ - 2}}$

$ \Rightarrow $ $1 = \frac{1}{r} + \frac{1}{{{r^2}}}$

$ \Rightarrow $ ${r^2} - r - 1 = 0$

$ \Rightarrow $ $r = \frac{{1 \pm \sqrt {1 + 4} }}{2} = \frac{{1 + \sqrt 5 }}{2}$

Taking only $(+)$ sign . $(\because \;r > 1)$

If every term of a $G.P.$ with positive terms is the sum of its two previous terms, then the common ratio of the series is

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