Construct linear and exponential functions, including arithmetic/geometric sequences, from graphs, descriptions, or input-output pairs.
Construct an explicit geometric sequence rule
Problem
Construct the explicit geometric-sequence rule when term \(1\) is \(6\) and each term is doubled.
Big Picture
What this problem is really about
An explicit geometric rule records a first term and the number of times a common multiplier has been applied. We’ll translate doubling into a ratio and use n minus one in the exponent because term one has undergone zero multiplications. Checking the first two terms will verify both the exponent offset and the repeated factor.
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