SOLUTION: Can ANYONE help me with these two problems? Please! Type the general term for the following sequences: #1) 3, 9, 27, 81, 243, . . . __________ #2) 3/4, 6/5, 9/6, 12

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# 1



Notice that each term is increasing exponentially. So this sequence might be a geometric sequence. To find out, let's simply divide the terms.


First divide the 2nd term 9 by the 1st term 3 to get


Now divide the 3rd term 27 by the 2nd term 9 to get


Now divide the 4th term 81 by the 3rd term 27 to get


Now divide the 5th term 243 by the 4th term 81 to get


So if we pick ANY term and divide it by the previous term, we'll always get 3.

This is the common ratio between the terms. So this means that .



Now since we've started at 3, this means that



Since the general geometric sequence is , this means the sequence is

where starts at


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Answer:

So the sequence is where starts at

Note: if you want to start at , then you need to replace "n" with "n-1" to get the new sequence