Which recursive formula can be used to define this sequence for n > 1? 1, 4, 7, 10, 13, 16, ... Choices: (A)a = a + a - 3 (B)a = 4a (C)a = a - 3 (D)a = a + 3

Sequence Type: We have the sequence: 1, 4, 7, 10, 13, 16, ... 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 1 and 4. 4 - 1 = 3 Common difference (d): 3Recursive Formula: Identify the recursive formula for the given sequence. Substitute 3 for d in a_n = a_(n-1) + d. Recursive formula: a_n = a_(n-1) + 3Match with Choices: Match the recursive formula with the given choices. The correct choice is (D) a_n = a_(n-1) + 3.

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Which recursive formula can be used to define this sequence for n > 1? $\newline$ $\newline$ $1, 4, 7, 10, 13, 16, \ldots$ $\newline$ $\newline$ Choices: $\newline$ (A) $a_n = a_{n-1} + a_{n-2} - 3$ $\newline$ (B) $a_n = 4a_{n-1}$ $\newline$ (C) $a_n = a_{n-1} - 3$ $\newline$ (D) $a_n = a_{n-1} + 3$

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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

\newline

1, 4, 7, 10, 13, 16, \ldots

\newline

\newline

Choices:

\newline

(A)

a_n = a_{n-1} + a_{n-2} - 3

\newline

(B)

a_n = 4a_{n-1}

\newline

(C)

a_n = a_{n-1} - 3

\newline

(D)

a_n = a_{n-1} + 3

Sequence Type: We have the sequence: $1, 4, 7, 10, 13, 16, \ldots$ $\newline$ 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, $d$ . $\newline$ Two consecutive terms are $1$ and $4$ . $\newline$ $4 - 1 = 3$ $\newline$ Common difference ( $d$ ): $3$
Recursive Formula: Identify the recursive formula for the given sequence. $\newline$ Substitute $3$ for $d$ in $a_n = a_{n-1} + d$ . $\newline$ Recursive formula: $a_n = a_{n-1} + 3$
Match with Choices: Match the recursive formula with the given choices. $\newline$ The correct choice is $(D) a_n = a_{(n-1)} + 3$ .