Which recursive formula can be used to define this sequence for n > 1? -8, 4, 16, 28, 40, 52, ... Choices: (A)a = a + a + 12 (B)a = 1/12a (C)a = a + 12 (D)a = 7a

Analyze Sequence Type: Analyze the sequence to determine if it is arithmetic or geometric. The sequence given is -8, 4, 16, 28, 40, 52, ... To determine if it is arithmetic, we check if the difference between consecutive terms is constant. 4 - (-8) = 12, 16 - 4 = 12, 28 - 16 = 12, 40 - 28 = 12, 52 - 40 = 12 Since the difference is constant, the sequence is arithmetic with a common difference of 12.Identify Recursive Formula: Identify the recursive formula for the arithmetic sequence. Since the common difference is 12, the recursive formula will be of the form a_n = a_(n-1) + d, where d is the common difference. Substituting 12 for d, we get the recursive formula: a_n = a_(n-1) + 12Match with Choices: Match the recursive formula with the given choices. The correct recursive formula is a_n = a_(n-1) + 12. Comparing this with the given choices, we find that choice (C) a_n = a_(n-1) + 12 matches our formula.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Which recursive formula can be used to define this sequence for n > 1? $\newline$ $-8, 4, 16, 28, 40, 52, \ldots$ $\newline$ Choices: $\newline$ (A) $a_{n} = a_{n-1} + a_{n-1} + 12$ $\newline$ (B) $a_{n} = \frac{1}{12}a_{n-1}$ $\newline$ (C) $a_{n} = a_{n-1} + 12$ $\newline$ (D) $a_{n} = 7a_{n-1}$

View step-by-step help

Home

Math Problems

Algebra 1

Write a formula for a recursive sequence

Full solution

Q. Which recursive formula can be used to define this sequence for

n > 1

\newline

-8, 4, 16, 28, 40, 52, \ldots

\newline

Choices:

\newline

(A)

a_{n} = a_{n-1} + a_{n-1} + 12

\newline

(B)

a_{n} = \frac{1}{12}a_{n-1}

\newline

(C)

a_{n} = a_{n-1} + 12

\newline

(D)

a_{n} = 7a_{n-1}

Analyze Sequence Type: Analyze the sequence to determine if it is arithmetic or geometric. $\newline$ The sequence given is $-8, 4, 16, 28, 40, 52, \ldots$ $\newline$ To determine if it is arithmetic, we check if the difference between consecutive terms is constant. $\newline$ $4 - (-8) = 12$ , $16 - 4 = 12$ , $28 - 16 = 12$ , $40 - 28 = 12$ , $52 - 40 = 12$ $\newline$ Since the difference is constant, the sequence is arithmetic with a common difference of $12$ .
Identify Recursive Formula: Identify the recursive formula for the arithmetic sequence. $\newline$ Since the common difference is $12$ , the recursive formula will be of the form $a_n = a_{(n-1)} + d$ , where $d$ is the common difference. $\newline$ Substituting $12$ for $d$ , we get the recursive formula: $a_n = a_{(n-1)} + 12$
Match with Choices: Match the recursive formula with the given choices. $\newline$ The correct recursive formula is $a_n = a_{n-1} + 12$ . $\newline$ Comparing this with the given choices, we find that choice (C) $a_n = a_{n-1} + 12$ matches our formula.