SOLUTION: Can ANYONE help me with these two problems? Please! Type the general term for the following sequences: #1) 3, 9, 27, 81, 243, . . . _________

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

Question 202544: 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, 12/7, 15/8...
__________

Thanks,
Sarah
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
I'll do the first one to get you going

# 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

===============================================================

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

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