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

Given Formula: The formula given is an = 7an - 3 + 4an - 4.Determine Explicit or Recursive: To determine if the formula is explicit or recursive, we need to see if it defines an in terms of previous terms.Formula References Previous Terms: Since the formula for an includes an - 3 and an - 4, it defines the term an based on the previous terms in the sequence.Formula is Not Explicit: This means the formula is not explicit, because an explicit formula would give an directly without referencing previous terms.Formula is Recursive: Therefore, the formula is recursive because it defines each term in the sequence by referring back to one or more previous terms.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

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

View step-by-step help

Home

Math Problems

Precalculus

Identify a sequence as explicit or recursive

Full solution

Q. Which word best describes this formula for the sequence

a_n

\newline

\newline

a_n = 7a_{n - 3} + 4a_{n - 4}

\newline

\newline

Choices:

\newline

(A)explicit

\newline

(B)recursive

Given Formula: The formula given is $a_n = 7a_{n - 3} + 4a_{n - 4}$ .
Determine Explicit or Recursive: To determine if the formula is explicit or recursive, we need to see if it defines $a_n$ in terms of previous terms.
Formula References Previous Terms: Since the formula for $a_n$ includes an $a_{n - 3}$ and an $a_{n - 4}$ , it defines the term $a_n$ based on the previous terms in the sequence.
Formula is Not Explicit: This means the formula is not explicit, because an explicit formula would give $a_n$ directly without referencing previous terms.
Formula is Recursive: Therefore, the formula is recursive because it defines each term in the sequence by referring back to one or more previous terms.