Write arithmetic and geometric sequences explicitly and recursively; translate between forms and model situations.
Translate a recursive arithmetic rule into an explicit rule
Problem
Translate the recursive arithmetic rule \(a_1~=~4\); \(a_n~=~a_{n-1}~+~6\) into an explicit rule.
Big Picture
What this problem is really about
Translating an arithmetic recurrence means replacing repeated updates with a direct count of those updates. We’ll read the initial term and additive change from the recursive rule, note that term one has received no updates, and multiply the change by the number of transitions to term n. Comparing term two in both forms verifies the translation.
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