Which recursive formula can be used to define this sequence for n > 1? 5, 18, 31, 44, 57, 70, ... Choices: (A)a = a + 13 (B)a = a - 13 (C)a = a + a - 13 (D)a = 18/5a

Sequence Type: We have the sequence: 5, 18, 31, 44, 57, 70, ... 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. Two consecutive terms are 5 and 18. 18 - 5 = 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 a_n = a_(n-1) + d. Recursive formula: a_n = a_(n-1) + 13Match with Choices: Match the recursive formula with the given choices. The correct formula is a_n = a_(n-1) + 13. This matches choice (A) if we assume the missing subscript n in the choice (A) is a typo.

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Which recursive formula can be used to define this sequence for n > 1? $\newline$ $5, 18, 31, 44, 57, 70, \ldots$ $\newline$ Choices: $\newline$ (A) $a_n = a_{n-1} + 13$ $\newline$ (B) $a_n = a_{n-1} - 13$ $\newline$ (C) $a_n = a_{n-1} + a_{n-2} - 13$ $\newline$ (D) $a_n = \frac{18}{5}a_{n-1}$

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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, 18, 31, 44, 57, 70, \ldots

\newline

Choices:

\newline

(A)

a_n = a_{n-1} + 13

\newline

(B)

a_n = a_{n-1} - 13

\newline

(C)

a_n = a_{n-1} + a_{n-2} - 13

\newline

(D)

a_n = \frac{18}{5}a_{n-1}

Sequence Type: We have the sequence: $5, 18, 31, 44, 57, 70, \ldots$ $\newline$ 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, $d$ . Two consecutive terms are $5$ and $18$ . $18 - 5 = 13$ 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 $a_n = a_{n-1} + d$ . $\newline$ Recursive formula: $a_n = a_{n-1} + 13$
Match with Choices: Match the recursive formula with the given choices. $\newline$ The correct formula is $a_n = a_{n-1} + 13$ . $\newline$ This matches choice $(A)$ if we assume the missing subscript $n$ in the choice $(A)$ is a typo.