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Solution: This is a geometric progression where each generation doubles the number of new infections. The initial case (generation 0) infects 2 people in generation 1, each of whom infects 2 more, and so on for 5 generations. The total number of infected people is the sum of a geometric series:
Let $ a = 1 $ (the original infected person), and each person infects 2 others, so the common ratio $ r = 2 $, and there are 6 terms (generations 0 through 5):
Question: An astronomer observes a planetary system where planets form at distances from the star following a pattern: every 3rd exoplanet orbits in a zone identified as habitable-like, and within those, exactly one-third of those are confirmed to support liquid water. If 108
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