What is the 7th term of this geometric sequence 2, 6, 18, 54, …?

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Answer 1 · 2018-06-24T01:36:56

#1458#

How do we get from #2# to #6#? One way is to multiply by #3#.

How do we get from #6# to #18#? We can multiply by #3# once again.

What about #18# to #54#? Again, we can multiply by #3#.

We notice that our common ratio is #3#. We can leverage this fact to write the next terms of our sequence:

#...54, (54*3), (54*3^2), color(blue)((54*3^3))#

Notice, we are multiplying by three every time. The #7#th term of this sequence is given by the blue expression

#54*3^3#, which is equal to

#54*27=color(blue)(1458)#

Hope this helps!