Which recursive formula can be used to define this sequence for n > 1? 15, 28, 41, 54, 67, 80, ... Choices: (A)a = a + 13 (B)a = 1/13a (C)a = 27/14a (D)a = a + a - 13

Sequence Type: We have the sequence: 15, 28, 41, 54, 67, 80, ... Is the given sequence geometric or arithmetic? The difference between consecutive terms is the same. The given sequence is arithmetic.Find Common Difference: Find the common difference, d, by subtracting two consecutive terms. For example, take the second term and subtract the first term: 28 - 15 = 13 Common difference (d): 13Recursive Formula: Identify the recursive formula for the given sequence. Since the sequence is arithmetic, the recursive formula will have the form a_n = a_(n-1) + d. Substitute 13 for d in the formula. Recursive formula: a_n = a_(n-1) + 13Match Formula with Choices: Match the recursive formula with the given choices. The correct choice that matches the formula a_n = a_(n-1) + 13 is: (A) a = a + 13 However, this choice is not correctly written. It should be a_n = a_(n-1) + 13, not a = a + 13.

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? $\newline$ $15, 28, 41, 54, 67, 80, \ldots$ $\newline$ Choices: $\newline$ (A) $a_{n} = a_{n-1} + 13$ $\newline$ (B) $a_{n} = \frac{1}{13}a_{n-1}$ $\newline$ (C) $a_{n} = \frac{27}{14}a_{n-1}$ $\newline$ (D) $a_{n} = a_{n-1} + a_{n-1} - 13$

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

15, 28, 41, 54, 67, 80, \ldots

\newline

Choices:

\newline

(A)

a_{n} = a_{n-1} + 13

\newline

(B)

a_{n} = \frac{1}{13}a_{n-1}

\newline

(C)

a_{n} = \frac{27}{14}a_{n-1}

\newline

(D)

a_{n} = a_{n-1} + a_{n-1} - 13

Sequence Type: We have the sequence: $15, 28, 41, 54, 67, 80, \ldots$ $\newline$ Is the given sequence geometric or arithmetic? $\newline$ The difference between consecutive terms is the same. $\newline$ The given sequence is arithmetic.
Find Common Difference: Find the common difference, $d$ , by subtracting two consecutive terms. $\newline$ For example, take the second term and subtract the first term: $28 - 15 = 13$ $\newline$ Common difference ( $d$ ): $13$
Recursive Formula: Identify the recursive formula for the given sequence. $\newline$ Since the sequence is arithmetic, the recursive formula will have the form $a_n = a_{n-1} + d$ . $\newline$ Substitute $13$ for $d$ in the formula. $\newline$ Recursive formula: $a_n = a_{n-1} + 13$
Match Formula with Choices: Match the recursive formula with the given choices. $\newline$ The correct choice that matches the formula $a_n = a_{n-1} + 13$ is: $\newline$ (A) $a = a + 13$ $\newline$ However, this choice is not correctly written. It should be $a_n = a_{n-1} + 13$ , not $a = a + 13$ .