A Geometric Sequence has 3rd term of 12 and 5th term of 48. What are the possible values for the common ratio?

1 Answer
Steve M
Sep 3, 2017

# +-2 #

Explanation:

Suppose the first term of the GP is #a#, and the common ratio is #r#, then the GP sequence would be :

# {a, ar, ar^2, ar^3, ..., ar^(n-1) } #

We are given that:

# 3^(rd) " term" = 12 => ar^2=12 # ..... [A]
# 5^(th) " term" = 48 => ar^4=48 # ..... [B]

Eq [B] #divide# Eq [A]:

#(ar^4)/(ar^2)=48/12 #
# :. r^2=4 #
# :. r=+-2 #

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