monarch,
The approach I used is that each term was being multiplied by some number. There were two patterns of multiples woven together. One pattern was constant - x 2. The other depends on the previous value (prev / 2).

1 x 5     = 5    # pattern 1, no prev value so start with 5
5 x 2     = 10   # pattern 2, constant
10 x 2.5  = 25   # pattern 1, prev value 5 / 2
25 x 2    = 50   # pattern 2, constant
50 x 1.25 = 62.5 # pattern 1, prev value 2.5 / 2
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