Derive and use the finite geometric series formula to solve problems such as mortgage-payment models.
Identify and verify a finite geometric series
Problem
For \(4~+~12~+~36~+~108~+~324\), state the first term, verify the common ratio with consecutive quotients, and count the terms.
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What this problem is really about
A finite series is geometric only if every forward consecutive quotient is the same, including its sign. Read the first term from the first addend and verify the ratio with more than one pair. Count the addends themselves, not the gaps between them, since a list with n terms has only n minus one transitions.
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