Question 46789
The length of the nth swing is 0.89 times the length of the (n-1)th swing.
Let the length of the nth swing be {{{L[n]}}}.
{{{L[1]=70}}}
{{{L[2]=0.89(70)}}}
{{{L[3]=0.89(0.89(70))=0.89^2(70)}}}
{{{L[4]=0.89(0.89(0.89(70)))=0.89^3(70)}}}
See a pattern emerging yet?
The formula for the length of the nth swing is {{{L[n]=70(0.89^((n-1)))}}}
So The length of the 9th swing is......
{{{L[9]=70(0.89^8)}}}
which is 27.56 inches, to 2 decimal places.


I hope this helps,
Adam
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