Which word best describes this formula for the sequence an? an = 87n^3 - 76n^2 - 78n Choices: (A)explicit (B)recursive

Examine Formula: Look at the formula: a_n = 87n^3 - 76n^2 - 78n. Does it use previous terms of the sequence to find the nth term? No, it doesn't. It uses the index n directly.Identify Recursion: Since the formula gives a direct way to find any term of the sequence using the index n, it's not recursive. A recursive formula would need the previous term(s) to find the next one.Determine Explicit Formula: So, the formula a_n = 87n^3 - 76n^2 - 78n is an explicit formula. It directly calculates the nth term without needing the 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 $a_n$ ? $\newline$ $\newline$ $a_n = 87n^3 - 76n^2 - 78n$ $\newline$ $\newline$ Choices: $\newline$ (A)explicit $\newline$ (B)recursive $\newline$

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

\newline

a_n = 87n^3 - 76n^2 - 78n

\newline

\newline

Choices:

\newline

(A)explicit

\newline

(B)recursive

\newline

Examine Formula: Look at the formula: $a_n = 87n^3 - 76n^2 - 78n$ . Does it use previous terms of the sequence to find the $n$ th term? No, it doesn't. It uses the index $n$ directly.
Identify Recursion: Since the formula gives a direct way to find any term of the sequence using the index $n$ , it's not recursive. $\newline$ A recursive formula would need the previous term(s) to find the next one.
Determine Explicit Formula: So, the formula $a_n = 87n^3 - 76n^2 - 78n$ is an explicit formula. $\newline$ It directly calculates the $n$ th term without needing the previous terms.