Which word best describes this formula for the sequence an? an = -2an - 1 - 4an - 4 + 10n - 3 Choices: (A)explicit (B)recursive

Formula Analysis: Look at the formula: a_n = -2a_(n-1) - 4a_(n-4) + 10n - 3. Does it use previous terms of the sequence? Yes, it uses a_(n-1) and a_(n-4), which are earlier terms in the sequence.Explicit vs Recursive: Since the formula for a_n depends on previous terms of the sequence, it's not explicit. An explicit formula would directly define a_n in terms of n alone.Correct Terminology: The correct word to describe the formula is ＂recursive＂ because it defines each term using previous terms in the sequence.

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Which word best describes this formula for the sequence $a_n$ ? $\newline$ $a_n = -2a_{n - 1} - 4a_{n - 4} + 10n - 3$ $\newline$ 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

\newline

a_n = -2a_{n - 1} - 4a_{n - 4} + 10n - 3

\newline

Choices:

\newline

(A)explicit

\newline

(B)recursive

\newline

Formula Analysis: Look at the formula: $a_n = -2a_{n-1} - 4a_{n-4} + 10n - 3$ . Does it use previous terms of the sequence? Yes, it uses $a_{n-1}$ and $a_{n-4}$ , which are earlier terms in the sequence.
Explicit vs Recursive: Since the formula for $a_n$ depends on previous terms of the sequence, it's not explicit. An explicit formula would directly define $a_n$ in terms of $n$ alone.
Correct Terminology: The correct word to describe the formula is ＂recursive＂ because it defines each term using previous terms in the sequence.