Posted by **Kim** on Saturday, October 6, 2012 at 9:17pm.

Please find the next THREE numbers in the patterns and explain how you got them:

1) 5, 5/2, 5/4, 5/8, 5/16....

2) 1, -3, 9, -27, 81...

3) 1/2, 1/2, 3/8, 1/4, 5/32...

4) -9, 101, -999, 10001, -99999...

- Math -
**Reiny**, Sunday, October 7, 2012 at 12:47am
1. each new number is 1/2 times the previous one ..

2. How about (-3)^n , were n = 0,1,2,3,...

3. What if I rewrote you fractions as

1/2 , 2/4, 3/8 , 4/16, 5/32 ...

Can you see what is happening ?

4. the odd-position numbers are all negative and contain as many 9's as the position in the sequence

e.g. the 7h number would be 9999999 (7 nines)

the even-position numbers are all positive and start and end with 1, with one less 0 between them as then position of the number

e.g. the 6th number is 1000001 (five 0's between the 1's)

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