Question
In a G.P. $729, 243, 81, …$ find $t_7$
✓
Answer
$\text { G.P }=729,243,81, \ldots .$
$ t _7=?$
$ t _{ n }= ar ^{ n -1}, \text { here } a =729, r =\frac{ t _2}{ t _1}$
$ r =\frac{243}{729}=\frac{1}{3}$
$ \therefore t _7=729\left(\frac{1}{3}\right)^{7-1}=729 \times\left(\frac{1}{3}\right)^6$
$ =729 \times \frac{1}{729}$
$ =1$
$ t _7=?$
$ t _{ n }= ar ^{ n -1}, \text { here } a =729, r =\frac{ t _2}{ t _1}$
$ r =\frac{243}{729}=\frac{1}{3}$
$ \therefore t _7=729\left(\frac{1}{3}\right)^{7-1}=729 \times\left(\frac{1}{3}\right)^6$
$ =729 \times \frac{1}{729}$
$ =1$
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