Which recursive formula can be used to define this sequence for n > 1? 2, 6, 10, 14, 18, 22, ... Choices: (A)a = a + 4 (B)a = a + a + 4 (C)a = 7/3a (D)a = a - 4

Sequence Type: We have the sequence: 2, 6, 10, 14, 18, 22, ... Is the given sequence geometric or arithmetic? The difference between consecutive terms is the same. The given sequence is arithmetic.Find Common Difference: Find the common difference, d. Two consecutive terms are 2 and 6. 6 - 2 = 4 Common difference (d): 4Recursive Formula: Identify the recursive formula for the given sequence. Substitute 4 for d in a_n = a_(n-1) + d. Recursive formula: a_n = a_(n-1) + 4

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Which recursive formula can be used to define this sequence for n > 1? $\newline$ $2, 6, 10, 14, 18, 22, \ldots$ $\newline$ Choices: $\newline$ (A) $a_n = a_{n-1} + 4$ $\newline$ (B) $a_n = a_{n-1} + a_{n-1} + 4$ $\newline$ (C) $a_n = \frac{7}{3}a_{n-1}$ $\newline$ (D) $a_n = a_{n-1} - 4$

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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, 6, 10, 14, 18, 22, \ldots

\newline

Choices:

\newline

(A)

a_n = a_{n-1} + 4

\newline

(B)

a_n = a_{n-1} + a_{n-1} + 4

\newline

(C)

a_n = \frac{7}{3}a_{n-1}

\newline

(D)

a_n = a_{n-1} - 4

Sequence Type: We have the sequence: $2, 6, 10, 14, 18, 22, \ldots$ $\newline$ 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 $2$ and $6$ . $\newline$ $6 - 2 = 4$ $\newline$ Common difference ( $d$ ): $4$
Recursive Formula: Identify the recursive formula for the given sequence. $\newline$ Substitute $4$ for $d$ in $a_n = a_{(n-1)} + d$ . $\newline$ Recursive formula: $a_n = a_{(n-1)} + 4$