Define a#b as the arithmetic mean of a and b. What is the value of ((1#2)#2)#4? Express your answer as a common fraction.
The hashtag is just a sign. Thank you!
so a#b =(a+b)/2
then
((1#2)#2)#4
= (1.5#2)#4
= 1.75#4
= 2.875
or
= 23/8
or
((1#2)#2)#4
= (3/2#2)#4
= (7/4)#4
= 23/8
To find the value of ((1#2)#2)#4, we need to evaluate each instance of the hashtag operation step by step.
Let's start with the first operation, 1#2. According to the given definition, the arithmetic mean of 1 and 2 is (1+2)/2 = 3/2.
Now, we have (3/2)#2. Again, applying the definition of the hashtag operation, the arithmetic mean of 3/2 and 2 is ((3/2)+2)/2 = (7/2)/2 = 7/4.
Moving forward, we have (7/4)#4. Applying the definition once more, the arithmetic mean of 7/4 and 4 is ((7/4)+4)/2 = (11/4)/2 = 11/8.
Therefore, the value of ((1#2)#2)#4 is 11/8.