Which recursive formula can be used to define this sequence for n > 1? 5, 19, 33, 47, 61, 75, ... Choices: (A)a = a + a - 14 (B)a = a + 14 (C)a = 14a (D)a = 19/5a

Identify Sequence Type: We have the sequence: 5, 19, 33, 47, 61, 75, ... Is the given sequence geometric or arithmetic? The difference between consecutive terms appears to be constant. The given sequence is likely 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: 19 - 5 = 14. Common difference (d): 14.Identify Recursive 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 14 for d in the formula. Recursive formula: a_n = a_(n-1) + 14.Match with Choices: Match the recursive formula with the given choices. The correct formula is (B) a_n = a_(n-1) + 14.

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? $\newline$ $5, 19, 33, 47, 61, 75, \ldots$ $\newline$ Choices: $\newline$ (A) $a_n = a_{n-1} + a_{n-2} - 14$ $\newline$ (B) $a_n = a_{n-1} + 14$ $\newline$ (C) $a_n = 14a_{n-1}$ $\newline$ (D) $a_n = \frac{19}{5}a_{n-1}$

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

5, 19, 33, 47, 61, 75, \ldots

\newline

Choices:

\newline

(A)

a_n = a_{n-1} + a_{n-2} - 14

\newline

(B)

a_n = a_{n-1} + 14

\newline

(C)

a_n = 14a_{n-1}

\newline

(D)

a_n = \frac{19}{5}a_{n-1}

Identify Sequence Type: We have the sequence: $5, 19, 33, 47, 61, 75, \ldots$ $\newline$ Is the given sequence geometric or arithmetic? $\newline$ The difference between consecutive terms appears to be constant. $\newline$ The given sequence is likely 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: $19 - 5 = 14$ . $\newline$ Common difference ( $d$ ): $14$ .
Identify 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 $14$ for $d$ in the formula. $\newline$ Recursive formula: $a_n = a_{n-1} + 14$ .
Match with Choices: Match the recursive formula with the given choices. $\newline$ The correct formula is $(B) a_n = a_{(n-1)} + 14$ .