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Define $a \ \# \ b$ as the arithmetic mean of $a$ and $b$. What is the value of $((1\ \#\ 2)\ \#\ 3) \ \# \ 4$? Express your answer as a common fraction.

 Jul 18, 2021
 #1
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I'm sure this is a trick question, but I guess I can try.

 

Order of operations first:

 

mean of 1 and 2 is 

 

\((1+2)/2=1.5\)

 

mean of 1.5 and 3 is

 

\((1.5+3)/2 =4.5/2 =2.25\)

 

mean of 2.25 and 4 is

 

\((2.25+4)/2 =6.25/2 =3.125\)

 

so the final answer is \(\fbox{3.125}\)

 Jul 18, 2021
edited by PBJcatalinasandwich  Jul 18, 2021

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