Which recursive formula can be used to define this sequence for n > 1? 15, 22, 29, 36, 43, 50, ... Choices: (A)a = a + 7 (B)a = a + a - 7 (C)a = 22/15a (D)a = a + a + 7

Sequence Type: We have the sequence: 15, 22, 29, 36, 43, 50, ... Is the given sequence geometric or arithmetic? The difference between consecutive terms appears to be constant. The given sequence is likely arithmetic.Find Common Difference: Find the common difference, d, by subtracting two consecutive terms. For example, take the second term and subtract the first term: 22 - 15 = 7 Common difference (d): 7Recursive Formula: Identify the recursive formula for the given sequence. Since the sequence is arithmetic, the recursive formula will have the form a_n = a_(n-1) + d, where d is the common difference. Substitute 7 for d in the formula. Recursive formula: a_n = a_(n-1) + 7Match with Choices: Match the recursive formula we found with the given choices. The correct choice is (A)a_n = a_(n-1) + 7.

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Which recursive formula can be used to define this sequence for n > 1? $\newline$ $15, 22, 29, 36, 43, 50, \ldots$ $\newline$ Choices: $\newline$ (A) $a_{n} = a_{n-1} + 7$ $\newline$ (B) $a_{n} = a_{n-1} + a_{n-1} - 7$ $\newline$ (C) $a_{n} = \frac{22}{15}a_{n-1}$ $\newline$ (D) $a_{n} = a_{n-1} + a_{n-1} + 7$

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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

15, 22, 29, 36, 43, 50, \ldots

\newline

Choices:

\newline

(A)

a_{n} = a_{n-1} + 7

\newline

(B)

a_{n} = a_{n-1} + a_{n-1} - 7

\newline

(C)

a_{n} = \frac{22}{15}a_{n-1}

\newline

(D)

a_{n} = a_{n-1} + a_{n-1} + 7

Sequence Type: We have the sequence: $15, 22, 29, 36, 43, 50, \ldots$ $\newline$ Is the given sequence geometric or arithmetic? $\newline$ The difference between consecutive terms appears to be constant. $\newline$ The given sequence is likely arithmetic.
Find Common Difference: Find the common difference, $d$ , by subtracting two consecutive terms. $\newline$ For example, take the second term and subtract the first term: $22 - 15 = 7$ $\newline$ Common difference ( $d$ ): $7$
Recursive Formula: Identify the recursive formula for the given sequence. $\newline$ Since the sequence is arithmetic, the recursive formula will have the form $a_n = a_{n-1} + d$ , where $d$ is the common difference. $\newline$ Substitute $7$ for $d$ in the formula. $\newline$ Recursive formula: $a_n = a_{n-1} + 7$
Match with Choices: Match the recursive formula we found with the given choices. $\newline$ The correct choice is $(A) a_n = a_{(n-1)} + 7$ .