Which recursive formula can be used to define this sequence for n > 1? 2, 4, 6, 8, 10, 12, ... Choices: (A)a = a - 2 (B)a = a + a - 2 (C)a = a + 2 (D)a = 2a

Given Sequence Type: We have: 2, 4, 6, 8, 10, 12, ... Is the given sequence geometric or arithmetic? The difference between consecutive terms is the same. The given sequence is arithmetic.Find Common Difference: 2, 4, 6, 8, 10, 12, ... Find the common difference, d. Two consecutive terms are 2 and 4. 4 - 2 = 2 Common difference (d): 2Recursive Formula Identification: 2, 4, 6, 8, 10, 12, ... Identify the recursive formula for the given sequence. Substitute 2 for d in a_n = a_(n-1) + d. Recursive formula: a_n = a_(n-1) + 2

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Which recursive formula can be used to define this sequence for n > 1? $\newline$ $2, 4, 6, 8, 10, 12, \ldots$ $\newline$ Choices: $\newline$ (A) $a_n = a_{n-1} - 2$ $\newline$ (B) $a_n = a_{n-1} + a_{n-1} - 2$ $\newline$ (C) $a_n = a_{n-1} + 2$ $\newline$ (D) $a_n = 2a_{n-1}$

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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

2, 4, 6, 8, 10, 12, \ldots

\newline

Choices:

\newline

(A)

a_n = a_{n-1} - 2

\newline

(B)

a_n = a_{n-1} + a_{n-1} - 2

\newline

(C)

a_n = a_{n-1} + 2

\newline

(D)

a_n = 2a_{n-1}

Given Sequence Type: We have: $2, 4, 6, 8, 10, 12, \ldots$ $\newline$ 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: $2, 4, 6, 8, 10, 12, \ldots$ $\newline$ Find the common difference, $d$ . $\newline$ Two consecutive terms are $2$ and $4$ . $\newline$ $4 - 2 = 2$ $\newline$ Common difference $(d): 2$
Recursive Formula Identification: $2, 4, 6, 8, 10, 12, \ldots$ $\newline$ Identify the recursive formula for the given sequence. $\newline$ Substitute $2$ for $d$ in $a_n = a_{n-1} + d$ . $\newline$ Recursive formula: $a_n = a_{n-1} + 2$