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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) $a_n = 11a_{n-1}$ $\newline$ (B) $a_n = a_{n-1} + a_{n-1} + 5$ $\newline$ (C) $a_n = a_{n-1} + 5$ $\newline$ (D) $a_n = \frac{1}{5}a_{n-1}$

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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 = 11a_{n-1}

\newline

(B)

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

\newline

(C)

a_n = a_{n-1} + 5

\newline

(D)

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

Given Sequence Type: We have: $-4, 1, 6, 11, 16, 21, \ldots$ $\newline$ 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: $-4, 1, 6, 11, 16, 21, \ldots$ $\newline$ Find the common difference, $d$ . $\newline$ Two consecutive terms are $-4$ and $1$ . $\newline$ $1 - (-4) = 5$ $\newline$ Common difference ( $d$ ): $5$
Identify Recursive Formula: $-4, 1, 6, 11, 16, 21, \ldots$ $\newline$ Identify the recursive formula for the given sequence. $\newline$ Substitute $5$ for $d$ in $a_n = a_{(n-1)} + d$ . $\newline$ Recursive formula: $a_n = a_{(n-1)} + 5$

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