Which recursive formula can be used to define this sequence for n > 1? 5, 18, 31, 44, 57, 70, ... Choices: (A)a = a + a - 13 (B)a = a - 13 (C)a = 18/5a (D)a = a + 13

Determine Sequence Type: We need to determine if the sequence is arithmetic or geometric. To do this, we look at the difference between consecutive terms.Calculate Difference: The first two terms are 5 and 18. The difference between them is 18 - 5 = 13.Check Consistency: We check if this difference is consistent by looking at the next pair of consecutive terms: 18 and 31. The difference is 31 - 18 = 13.Sequence Type Conclusion: Since the difference between consecutive terms is consistent, we can conclude that the sequence is arithmetic with a common difference of 13.Find Recursive Formula: To find the recursive formula for an arithmetic sequence, we use the formula a_n = a_(n-1) + d, where d is the common difference.Substitute Common Difference: Substituting the common difference of 13 into the formula, we get the recursive formula a_n = a_(n-1) + 13.

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Which recursive formula can be used to define this sequence for n > 1? $\newline$ $5, 18, 31, 44, 57, 70, \ldots$ $\newline$ Choices: $\newline$ (A) $a_n = a_{n-1} + a_{n-2} - 13$ $\newline$ (B) $a_n = a_{n-1} - 13$ $\newline$ (C) $a_n = \frac{18}{5}a_{n-1}$ $\newline$ (D) $a_n = a_{n-1} + 13$

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Math Problems

Algebra 1

Write a formula for a recursive sequence

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Q. Which recursive formula can be used to define this sequence for

n > 1

\newline

5, 18, 31, 44, 57, 70, \ldots

\newline

Choices:

\newline

(A)

a_n = a_{n-1} + a_{n-2} - 13

\newline

(B)

a_n = a_{n-1} - 13

\newline

(C)

a_n = \frac{18}{5}a_{n-1}

\newline

(D)

a_n = a_{n-1} + 13

Determine Sequence Type: We need to determine if the sequence is arithmetic or geometric. To do this, we look at the difference between consecutive terms.
Calculate Difference: The first two terms are $5$ and $18$ . The difference between them is $18 - 5 = 13$ .
Check Consistency: We check if this difference is consistent by looking at the next pair of consecutive terms: $18$ and $31$ . The difference is $31 - 18 = 13$ .
Sequence Type Conclusion: Since the difference between consecutive terms is consistent, we can conclude that the sequence is arithmetic with a common difference of $13$ .
Find Recursive Formula: To find the recursive formula for an arithmetic sequence, we use the formula $a_n = a_{n-1} + d$ , where $d$ is the common difference.
Substitute Common Difference: Substituting the common difference of $13$ into the formula, we get the recursive formula $a_n = a_{n-1} + 13$ .