Write arithmetic and geometric sequences explicitly and recursively; translate between forms and model situations.
Write an explicit arithmetic sequence rule from terms
Problem
Write an explicit arithmetic-sequence rule for the terms \(5,~8,~11,~14\).
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What this problem is really about
An explicit arithmetic rule reaches any term from its index without generating the earlier list. We’ll identify the first term and verify the common difference, then count how many equal transitions occur from term one to term n. The one-less-than-the-index count is crucial, and substituting both the first and a later index will test it.
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