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

Examine Formula: Look at the formula: a_n = -4a_(n-1) - 3a_(n-3) + 10n^2 + 4. 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.Use of Previous Terms: Since the formula uses previous terms, it's not explicit. Explicit formulas give the nth term without needing earlier terms.Explicit vs. Recursive: So, the formula is recursive because it defines each term using previous terms in the sequence.

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 $a_n$ ? $\newline$ $a_n = -4a_{n - 1} - 3a_{n - 3} + 10n^2 + 4$ $\newline$ Choices: $\newline$ (A)explicit $\newline$ (B)recursive

View step-by-step help

Home

Math Problems

Algebra 1

Identify a sequence as explicit or recursive

Full solution

Q. Which word best describes this formula for the sequence

a_n

\newline

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

\newline

Choices:

\newline

(A)explicit

\newline

(B)recursive

Examine Formula: Look at the formula: $a_n = -4a_{n-1} - 3a_{n-3} + 10n^2 + 4$ . 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.
Use of Previous Terms: Since the formula uses previous terms, it's not explicit. Explicit formulas give the $n$ th term without needing earlier terms.
Explicit vs. Recursive: So, the formula is recursive because it defines each term using previous terms in the sequence.