The #n#th term #u_n# of a geometric sequence is given by #u_n = 3(4)^(n+1)#, #n in ZZ^+#. What is the common ratio #r#?

Question

I supposed #r# might be #4# but the #n#th term of a geometric sequence is normally given by #u_n = u_1*r^(n-1)#, but in the question #4# has a power of #n+1# so I'm confused by #n+1# and #n-1#

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Answer 1 · 2017-11-25T16:33:50

# 4.#

The Common Ratio #r# of a Geometric Sequence

#{u_n=u_1*r^(n-1) : n in ZZ^+}# is given by,

#r=u_(n+1) -: u_n.............(ast).#

Since, #u_n=3*4^(n+1),# we have, by #(ast),#

#r={3*4^((n+1)+1)}-:{3*4^(n+1)}.#

# rArr r=4.#