The first term in a certain geometric sequence is x and the fourth term in the sequence is 27x, where x is a nonzero number. Which of the following represents the tenth term?

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Answer 1 · 2018-04-19T09:09:22

#color(blue)(x(3)^9)#

The nth term of a geometric sequence is given as:

#ar^(n-1)#

Where:

#bba# is the first term, #bbr# is the common ratio and #bbn# is the nth term.

First term is #x#

Fourth term is #27x#

Using this:

#xr^(4-1)=27x#

#r^3=27#

#r=root(3)(r^3)=root(3)(27)=3#

10th term:

#n_(10) =x(3)^(10-1)=color(blue)(x(3)^9)#