My Discrete Math students today came up with an observation: The
average of any 3 consecutive terms of an arithmetic sequence equals
the middle term. So, I thought we'd show off some CAS in SAGE (this
class uses python primarily) and wrote the following in my SAGE
notebook:
var('c,d')
term1 = c+(n-1)*d
term2 = c+(n+1)*d
sum = term1+term2
avg = expand(sum/2)
show(term1)
show(term2)
show(sum)
show(avg)
and got the following output
c+(n-1)*d
c+(n+1)*d
2*c+2*n*d
c+n*d
So, I thought we'd try something similar with geometric sequences:
var('c,d')
term1 =a*r**(n-1)
term2 = a*r*(n+1)
prod = term1*term2
avg = simplify(sqrt(prod))
show(term1)
show(term2)
show(sum)
show(avg)
however, I got the following output
a*r**(n-1)
a*r*(n+1)
a**2*r**(2*n)
sqrt(a**2*r**(2*n))
I couldn't get the final result to reduce to a*r**n, is there a way to
do this?
TIA,
A. Jorge Garcia
http://shadowfaxrant.blogspot.com
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