Qthere are two rabbit's in a park .if they double their number every month after how many months theirnumberwill be 64

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$$\begin{gathered} \mathrm{They} \mathrm{are} 2 \mathrm{rabbits} \mathrm{in} \mathrm{first} \mathrm{month}. \\ \mathrm{Hence} \mathrm{first} \mathrm{term}=\mathrm{a}=2 \\ \mathrm{They} \mathrm{double} \mathrm{their} \mathrm{count} \mathrm{every} \mathrm{month}, \mathrm{hence} \\ \mathrm{Common} \mathrm{ratio}=\mathrm{r}=2 \\ \mathrm{Hence} \mathrm{let} {\mathrm{r}}_{\mathrm{th}} \mathrm{term} \mathrm{be} 64 \\ \mathrm{Hence} \\ {\mathrm{T}}_{\mathrm{r}}={\mathrm{ar}}^{\mathrm{r}-1} \\ 64=2\times {\left(2\right)}^{\mathrm{r}-1} \\ \Rightarrow {\left(2\right)}^{\mathrm{r}-1}=32=2^5 \\ \mathrm{r}-1=5 \\ \mathrm{r}=6 \\ \mathrm{Hence} \mathrm{after} 6\mathrm{th} \mathrm{month} \mathrm{their} \mathrm{count} \mathrm{will} \mathrm{be} 64. \end{gathered}$$

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