The Golden Prediction example

 1. 10
 2. 22 (22 + 10) = 32
 3. 32 (32 + 22) = 54
 4. 54 (32 + 54) = 86, etc.
 5. 86
 6. 140
 7. 226
 8. 366
 9. 592
10. 958
11. 1550
12. 2508
13. 4058 
14. 6566
15. 10624
16. 17190
17. 27814
18. 45004
19. 72818
20. 117822
21. 190640
22. 308462
23. 499102
24. 807564
25. 1306666

Select any number among the last five on the list, 
and divide by the number above it. 

For example, divide #24 by #23:

807564/499102 = 1.618033989....