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Which recursive formula can be used to define this sequence for $n > 1$ ? $\newline$ $9, 19, 29, 39, 49, 59, \ldots$ $\newline$ Choices: $\newline$ (A) $a = a + a + 10$ $\newline$ (B) $a = 10a$ $\newline$ (C) $a = a + 10$ $\newline$ (D) $a = \frac{19}{9}a$

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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

9, 19, 29, 39, 49, 59, \ldots

\newline

Choices:

\newline

(A)

a = a + a + 10

\newline

(B)

a = 10a

\newline

(C)

a = a + 10

\newline

(D)

a = \frac{19}{9}a

Sequence Type: We have the sequence: $9, 19, 29, 39, 49, 59, \ldots$ $\newline$ 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 any term from the term that follows it. $\newline$ For example, take the first two terms: $19$ and $9$ . $\newline$ $19 - 9 = 10$ $\newline$ Common difference ( $d$ ): $10$
Identify Recursive Formula: Identify the recursive formula for the given sequence. $\newline$ Since the sequence is arithmetic with a common difference of $10$ , the recursive formula will add $10$ to the previous term. $\newline$ The correct recursive formula is: $a_n = a_{n-1} + 10$
Match with Choices: Match the correct recursive formula with the given choices. $\newline$ The correct formula, $a_n = a_{n-1} + 10$ , matches choice $(C)$ .

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