Which word best describes this formula for the sequence an? an = 4an - 2 - 3an - 3 + 10n^2 + 3n - 7 Choices: (A)explicit (B)recursive

Examine Formula: Look at the formula: a_n = 4a_(n-2) - 3a_(n-3) + 10n^2 + 3n - 7. Does it use previous terms of the sequence to find the nth term? Yes, it uses a_(n-2) and a_(n-3), which are terms before a_n.Identify Recursion: Since the formula uses previous terms, it's not explicit. Explicit formulas give the nth term without needing earlier terms.Understand Explicit Formulas: So, the formula is recursive because it defines a term based on previous terms in the sequence.

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Which word best describes this formula for the sequence $a_n$ ? $\newline$ $\newline$ $a_n = 4a_{n - 2} - 3a_{n - 3} + 10n^2 + 3n - 7$ $\newline$ $\newline$ Choices: $\newline$ (A)explicit $\newline$ (B)recursive $\newline$

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Math Problems

Algebra 1

Identify a sequence as explicit or recursive

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Q. Which word best describes this formula for the sequence

a_n

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\newline

a_n = 4a_{n - 2} - 3a_{n - 3} + 10n^2 + 3n - 7

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\newline

Choices:

\newline

(A)explicit

\newline

(B)recursive

\newline

Examine Formula: Look at the formula: $a_n = 4a_{n-2} - 3a_{n-3} + 10n^2 + 3n - 7$ . Does it use previous terms of the sequence to find the nth term? Yes, it uses $a_{n-2}$ and $a_{n-3}$ , which are terms before $a_n$ .
Identify Recursion: Since the formula uses previous terms, it's not explicit. Explicit formulas give the $n^{\text{th}}$ term without needing earlier terms.
Understand Explicit Formulas: So, the formula is recursive because it defines a term based on previous terms in the sequence.