Which recursive formula can be used to define this sequence for n > 1? -4, 1, 6, 11, 16, 21, ... Choices: (A)a = a + 5 (B)a = 1/5a (C)a = a + a + 5 (D)a = 11a

Identify Sequence Type: We have the sequence: -4, 1, 6, 11, 16, 21, ... 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 -4 and 1. 1 - (-4) = 5 Common difference (d): 5Recursive Formula: Identify the recursive formula for the given sequence. Substitute 5 for d in a_n = a_(n-1) + d. Recursive formula: a_n = a_(n-1) + 5Match with Choices: Match the recursive formula with the given choices. The correct choice is (A)a_n = a_(n-1) + 5.

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Which recursive formula can be used to define this sequence for n > 1? $\newline$ $-4, 1, 6, 11, 16, 21, \ldots$ $\newline$ Choices: $\newline$ (A) $a_{n} = a_{n-1} + 5$ $\newline$ (B) $a_{n} = \frac{1}{5}a_{n-1}$ $\newline$ (C) $a_{n} = a_{n-1} + a_{n-1} + 5$ $\newline$ (D) $a_{n} = 11a_{n-1}$

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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

-4, 1, 6, 11, 16, 21, \ldots

\newline

Choices:

\newline

(A)

a_{n} = a_{n-1} + 5

\newline

(B)

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

\newline

(C)

a_{n} = a_{n-1} + a_{n-1} + 5

\newline

(D)

a_{n} = 11a_{n-1}

Identify Sequence Type: We have the sequence: $-4, 1, 6, 11, 16, 21, \ldots$ $\newline$ 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 $-4$ and $1$ . $1 - (-4) = 5$ Common difference ( $d$ ): $5$
Recursive Formula: Identify the recursive formula for the given sequence. $\newline$ Substitute $5$ for $d$ in $a_n = a_{n-1} + d$ . $\newline$ Recursive formula: $a_n = a_{n-1} + 5$
Match with Choices: Match the recursive formula with the given choices. $\newline$ The correct choice is $(A) a_n = a_{(n-1)} + 5$ .