How do you write a rule for the nth term of the geometric sequence given the two terms #a_2=4, a_5=256/27#?

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Answer 1 · 2018-06-26T09:48:49

#a_n = 3*(4/3)^(n-1) #

The geometric #n^"th" # term is #a_n = ar^(n-1) #

Where #a# is the first term

# ar = 4 #

# ar^4 = 256/27 #

#=> a = 4/r #

#=> 4/r * r^4 = 256/27 #

#=> 4r^3 = 256/27 #

#=> r = 4/3 #

#=> a = 4/r = 4/(4/3) = 3 #

#=> a_n = 3*(4/3)^(n-1) #