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Geometric Sequences

Check out this guy:

3 / 2 , -( 1 / 3 ) , 2 / 27 , -( 4 / 243 ) , ...

All of a sudden this isn't so funny!  Don't start to sweat yet.  It's really pretty easy...

Just crunch outa2 divided by a1:

a2 divided by a1 = -( 1 / 3 ) divided by ( 3 / 2 ) = -( 1 / 3 ) * ( 2 / 3 ) = -( 2 / 9 )

Probably the ratio...

To check, test it on the second term:

a2 * -( 2 / 9 ) = -( 1 / 3 ) * -( 2 / 9 ) = 2 / 27

Yep, it got us up toa3!

 ratio = -( 2 / 9 )
 

YOUR TURN:

Find the ratio:

15 / 2 , 5 , 10 / 3 , 20 / 9 , ...