Write arithmetic and geometric sequences explicitly and recursively; translate between forms and model situations.
Write an explicit geometric sequence rule from terms
Problem
Write an explicit geometric-sequence rule for the terms \(3\), \(6\), \(12\), \(24\).
Big Picture
What this problem is really about
An explicit geometric rule compresses repeated multiplication into a power. We’ll identify the first term, verify the common ratio from consecutive quotients, and count how many ratio applications separate term one from term n. The exponent must be zero at the first index, so checking the first and a later term exposes any indexing shift.
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