Which word best describes this formula for the sequence an? an = -4an - 1 + 5an - 4 + 19n + 3 Choices: (A)explicit (B)recursive

Examine Formula: Look at the formula: a_n = -4a_(n-1) + 5a_(n-4) + 19n + 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.Use of Previous Terms: Since the formula for a_n depends on previous terms of the sequence, it's not explicit. An explicit formula would directly calculate a_n based on n alone.Explicit vs. Recursive: The formula is recursive because it defines each term using previous terms in the sequence. So, the correct choice is (B) recursive.

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Which word best describes this formula for the sequence $a_n$ ? $\newline$ $a_n = -4a_{n - 1} + 5a_{n - 4} + 19n + 3$ $\newline$ Choices: $\newline$ (A)explicit $\newline$ (B)recursive

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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 = -4a_{n - 1} + 5a_{n - 4} + 19n + 3

\newline

Choices:

\newline

(A)explicit

\newline

(B)recursive

Examine Formula: Look at the formula: $a_n = -4a_{n-1} + 5a_{n-4} + 19n + 3$ . 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.
Use of Previous Terms: Since the formula for $a_n$ depends on previous terms of the sequence, it's not explicit. An explicit formula would directly calculate $a_n$ based on $n$ alone.
Explicit vs. Recursive: The formula is recursive because it defines each term using previous terms in the sequence. $\newline$ So, the correct choice is $(B)$ recursive.