Question

In the G.P. $729,243,81,$ ............ find $T_7$.

Answer 1

It is given that the first term of G.P is $a_1=729$ and the second term is $a_2=243$, therefore,

$r=\frac{a_2}{a_1}=\frac{243}{729}=\frac{1}{3}$

We know that the formula for the $n$th term of an G.P is $T_n=a{r}^{n-1}$, where $a$ is the first term, $r$ is the common ratio.

It is given that the first term is $a=729$ and the common ratio is $r=\frac{1}{3}$, thus,

$T_7=729\times {\left(\frac{1}{3}\right)}^{7-1}=729\times \frac{1}{3^6}=\frac{729}{729}=1$

Hence, $T_7=1$.