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Which recursive formula can be used to define this sequence for $n > 1$ ? $\newline$ $14, 16, 18, 20, 22, 24, \ldots$ $\newline$ Choices: $\newline$ (A) $a = a + a + 2$ $\newline$ (B) $a = \frac{8}{7}a$ $\newline$ (C) $a = a - 2$ $\newline$ (D) $a = a + 2$

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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

14, 16, 18, 20, 22, 24, \ldots

\newline

Choices:

\newline

(A)

a = a + a + 2

\newline

(B)

a = \frac{8}{7}a

\newline

(C)

a = a - 2

\newline

(D)

a = a + 2

Sequence Type: We have the sequence: $14, 16, 18, 20, 22, 24, \ldots$ $\newline$ 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 $14$ and $16$ . $\newline$ $16 - 14 = 2$ $\newline$ Common difference ( $d$ ): $2$
Recursive Formula: Identify the recursive formula for the given sequence. $\newline$ Substitute $2$ for $d$ in $a_n = a_{n-1} + d$ . $\newline$ Recursive formula: $a_n = a_{n-1} + 2$

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