SOLUTION: Find the general term and the 29th term of the sequence <img src="http://i293.photobucket.com/albums/mm56/cool_user2004/5-1.png" alt="Photobucket

SOLUTION: Find the general term and the 29th term of the sequence <img src="http://i293.photobucket.com/albums/mm56/cool_user2004/5-1.png" alt="Photobucket - Video and Image Hosting"

Question 172791: Find the general term and the 29th term of the sequence

Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Ignoring (for now) the term "6", what do you see happening here?

If we write as , then we have the sequence

, , 6, ,

It looks like the coefficients are increasing by 1 while the radicands (the stuff inside the square root) is 1 more than the coefficients. So if n=1, then the first term is , and if n=2 the second term is

So it appears that the sequence is simply (notice how the radicand is one more than the coefficient).

So take note how 6 is the 3rd term (so n=3). This means that (which confirms our answer)

So the sequence is for

So if, for example, , then the 4th term is

To find the 29th term, simply plug in

Start with the given sequence

Plug in

Add

From here, we cannot simplify any further.

So the 29th term is
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