Which recursive formula can be used to define this sequence for n > 1? 1, 15, 29, 43, 57, 71, ... Choices: (A)a = a - 14 (B)a = a + 14 (C)a = 43/15a (D)a = a + a - 14

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 Differences: The first two terms are 1 and 15. The difference between them is 15 - 1 = 14.Identify Arithmetic Sequence: The next two terms are 15 and 29. The difference between them is 29 - 15 = 14.Find Recursive Formula: Since the difference between consecutive terms is constant, we can conclude that the sequence is arithmetic with a common difference of 14.Substitute Common Difference: 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.Match with Correct Formula: Substituting the common difference of 14 into the formula, we get a_n = a_(n-1) + 14.Looking at the given choices, the correct recursive formula that matches our calculation is (B) a_n = a_(n-1) + 14.

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Which recursive formula can be used to define this sequence for n > 1? $\newline$ $\newline$ $1, 15, 29, 43, 57, 71, \ldots$ $\newline$ $\newline$ Choices: $\newline$ (A) $a_n = a_{n-1} - 14$ $\newline$ (B) $a_n = a_{n-1} + 14$ $\newline$ (C) $a_n = \frac{43}{15}a_n$ $\newline$ (D) $a_n = a_{n-1} + a_{n-1} - 14$

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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

\newline

1, 15, 29, 43, 57, 71, \ldots

\newline

\newline

Choices:

\newline

(A)

a_n = a_{n-1} - 14

\newline

(B)

a_n = a_{n-1} + 14

\newline

(C)

a_n = \frac{43}{15}a_n

\newline

(D)

a_n = a_{n-1} + a_{n-1} - 14

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 Differences: The first two terms are $1$ and $15$ . The difference between them is $15 - 1 = 14$ .
Identify Arithmetic Sequence: The next two terms are $15$ and $29$ . The difference between them is $29 - 15 = 14$ .
Find Recursive Formula: Since the difference between consecutive terms is constant, we can conclude that the sequence is arithmetic with a common difference of $14$ .
Substitute Common Difference: 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.
Match with Correct Formula: Substituting the common difference of $14$ into the formula, we get $a_n = a_{n-1} + 14$ .
Match with Correct Formula: Substituting the common difference of $14$ into the formula, we get $a_n = a_{n-1} + 14$ .Looking at the given choices, the correct recursive formula that matches our calculation is (B) $a_n = a_{n-1} + 14$ .