# Question #5db2a

Jul 3, 2017

$1$ foot wil remain after $5$ cuts.
${a}_{n + 1} = {a}_{1} \cdot {r}^{n}$ feet will remain after $n$ cuts .

#### Explanation:

1st term is ${a}_{1} = 243$ . Common ratio is $r = 1 - \frac{2}{3} = \frac{1}{3}$

This is series of geometric progression $\left(243 , 81 , 27 , 9 , 3 , 1. .\right)$

Number of terrms is $n = 5 + 1 = 6$ after $5$ cuts

$n$ th term is ${a}_{n} = {a}_{1} \cdot {r}^{n - 1} \therefore {a}_{6} = 243 \cdot {\left(\frac{1}{3}\right)}^{5} = 243 \cdot \frac{1}{243} = 1$foot

$1$ foot wil remain after $5$ cuts.

${a}_{n + 1} = {a}_{1} \cdot {r}^{n}$ feet will remain after $n$ cuts .[Ans]