Question

which word best describes this formula for the sequence $a_n$?
$a_n = 7a_{n - 1} + 2a_{n - 2} + 2a_{n - 4}$
explicit recursive

Explanation:

A recursive sequence formula defines a term using previous terms of the sequence. The given formula $a_n = 7a_{n-1} + 2a_{n-2} + 2a_{n-4}$ defines $a_n$ using earlier terms $a_{n-1}$, $a_{n-2}$, and $a_{n-4}$, which fits the definition of a recursive formula. An explicit formula would define $a_n$ directly in terms of $n$ without referencing prior terms.

Answer:

recursive