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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) $a = a + 5$ $\newline$ (B) $a = a + a + 5$ $\newline$ (C) $a = 11a$ $\newline$ (D) $a = \frac{1}{5}a$

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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 = a + 5

\newline

(B)

a = a + a + 5

\newline

(C)

a = 11a

\newline

(D)

a = \frac{1}{5}a

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, $d$ , by subtracting a term from the term that follows it. $\newline$ For example, take the second term ( $1$ ) and the first term ( $-4$ ): $\newline$ $1 - (-4) = 1 + 4 = 5$ $\newline$ Common difference ( $d$ ): $5$
Identify Recursive Formula: Identify the recursive formula for the given sequence. $\newline$ Since the common difference is $5$ , the recursive formula will add $5$ to the previous term to get the next term. $\newline$ The correct recursive formula is: $a_n = a_{(n-1)} + 5$
Match with Choices: Match the correct recursive formula with the given choices. $\newline$ The correct formula, $a_n = a_{n-1} + 5$ , corresponds to choice $(A)$ $a = a + 5$ .

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