Write arithmetic and geometric sequences explicitly and recursively; translate between forms and model situations.
Translate an explicit arithmetic rule into a recursive rule
Problem
Translate the explicit arithmetic rule \(a_n~=~7~+~3(n~-~1)\) into a recursive rule.
Big Picture
What this problem is really about
To turn an explicit arithmetic rule into a recurrence, recover the information needed for one-step generation. We’ll evaluate the formula at the first index to obtain the initial term, read the coefficient of the transition count as the common difference, and link each later term to its predecessor. Agreement at the second index checks both pieces.
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