Question #5db2a

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Answer 1 · 2017-07-03T11:47:34

$1$ $1$ foot wil remain after $5$ $5$ cuts.
$a_{n + 1} = a_{1} \cdot r^{n}$ $a_(n+1)=a_1*r^n$ feet will remain after $n$ $n$ cuts .

1st term is $a_{1} = 243$ $a_1=243$ . Common ratio is $r = 1 - \frac{2}{3} = \frac{1}{3}$ $r=1-2/3=1/3$

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

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

$n$ $n$ th term is $a_n=a_1*r^(n-1) :. a_6= 243*(1/3)^5=243*1/243=1$ foot

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

$a_(n+1)=a_1*r^n$ feet will remain after $n$ cuts .[Ans]