Which word best describes this formula for the sequence an? an = 6an - 1 + 2an - 3 + 14n + 3 Choices: (A)explicit (B)recursive

Examine the Formula: Look at the formula: a_n = 6a_(n-1) + 2a_(n-3) + 14n + 3. Does it use previous terms of the sequence? Yes, it uses a_(n-1) and a_(n-3), which are earlier terms in the sequence.Dependency on 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 from n without needing previous terms.Recursive Formula: 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 $a_n$ ? $\newline$ $a_n = 6a_{n - 1} + 2a_{n - 3} + 14n + 3$ $\newline$ 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 = 6a_{n - 1} + 2a_{n - 3} + 14n + 3

\newline

Choices:

\newline

(A) explicit

\newline

(B) recursive

Examine the Formula: Look at the formula: $a_n = 6a_{n-1} + 2a_{n-3} + 14n + 3$ . Does it use previous terms of the sequence? Yes, it uses $a_{n-1}$ and $a_{n-3}$ , which are earlier terms in the sequence.
Dependency on Previous Terms: Since the formula for $a_n$ depends on previous terms of the sequence, it's not explicit. $\newline$ An explicit formula would directly calculate $a_n$ from $n$ without needing previous terms.
Recursive Formula: The formula is recursive because it defines each term using previous terms in the sequence.