Question 840087
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1, 1, 9, 9,

Two 1's then two 9's, then 2 1's, then two 9's, over and over, etc.
That is:

1, 1, 9, 9, 1, 1, 9, 9, 1, 1, 9, 9, 1, 1, 9, 9,...

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1, 9, 9, 81, 

The first two terms are 1 and 9.

After that, each term is the product of the two preceding terms:

1, 9, 1×9=9, 9×9=81, 9×81=729, 81×729=59049, 729×59049=43046721, etc. 

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6, 0, 0, 0, ?

6, 0, 0, 0, 6, 0, 0, 0, 6, 0, 0, 0, 6, 0, 0, 0, etc.

6, then three zeros, then 6, then three zeros, then 6, then three zeros, etc. 

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5, 5, 25, 25, ?

The first two terms are 5's.  After that each pair of terms are both the next higher power of 5. 

5<sup>1</sup>, 5<sup>1</sup>, 5<sup>2</sup>, 5<sup>2</sup>, 5<sup>3</sup>, 5<sup>3</sup>, 5<sup>4</sup>, 5<sup>4</sup>, 5<sup>5</sup>, 5<sup>5</sup>, etc. 

 or

5, 5, 25, 25, 125, 125, 625, 625, 3125, 3125, etc.


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1, 2, 20, 40, ?

The first two terms are 1 and 2.

After that, the next two terms, respectively, are 20 times the preceding 
two terms, respectively.
  
1, 2, 20, 40, 400, 800, 8000, 16000, etc.

Edwin</pre>