Question

what is the common ratio of the geometric sequence whose 5th and 7th terms are 4 and 36 respectively​

Answer 1

Answer:

Common ratio r = 3

Step-by-step explanation:

Answer 2

Given,

The fifth term$\[ = 4\]$

The seventh term$\[ = 36\]$

Solution,

Formula used,$\[{T_n} = a{r^{n - 1}}.\]$

Assume that the first term is a and the common ratio is r.

Apply the given conditions.

$\[\begin{array}{l} \Rightarrow \frac{{36}}{4} = \frac{{a{r^{7 - 1}}}}{{a{r^{5 - 1}}}}\\ \Rightarrow 9 = \frac{{{r^6}}}{{{r^4}}}\\ \Rightarrow {r^2} = 9\\ \Rightarrow r = \pm 3\end{array}\]$

Hence, the common ratio is $\[ \pm 3.\]$