Which recursive formula can be used to define this sequence for n > 1? 1, 12, 23, 34, 45, 56, ... Choices: (A)a = a + 11 (B)a = 17/6a (C)a = a + a + 11 (D)a = a - 11

Sequence Type Determination: We have the sequence: 1, 12, 23, 34, 45, 56, ... To determine the type of sequence, we need to check the difference between consecutive terms.Calculate First Two Terms: Calculate the difference between the first two terms: 12 - 1 = 11.Calculate Second and Third Terms: Calculate the difference between the second and third terms: 23 - 12 = 11.Conclusion of Sequence Type: Since the difference between consecutive terms is constant, we can conclude that the sequence is an arithmetic sequence with a common difference of 11.Arithmetic Sequence Recursive Formula: The recursive formula for an arithmetic sequence is given by a_n = a_(n-1) + d, where d is the common difference.Substitute Common Difference: Substitute the common difference (11) into the recursive formula to get the specific formula for this sequence: a_n = a_(n-1) + 11.Comparison with Choices: Comparing the derived formula with the given choices, we find that the correct choice is (A)a_n = a_(n-1) + 11.

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Which recursive formula can be used to define this sequence for n > 1? $\newline$ $1, 12, 23, 34, 45, 56, \ldots$ $\newline$ Choices: $\newline$ (A) $a_n = a_{n-1} + 11$ $\newline$ (B) $a_n = \frac{17}{6}a_{n-1}$ $\newline$ (C) $a_n = a_{n-1} + a_{n-1} + 11$ $\newline$ (D) $a_n = a_{n-1} - 11$

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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

1, 12, 23, 34, 45, 56, \ldots

\newline

Choices:

\newline

(A)

a_n = a_{n-1} + 11

\newline

(B)

a_n = \frac{17}{6}a_{n-1}

\newline

(C)

a_n = a_{n-1} + a_{n-1} + 11

\newline

(D)

a_n = a_{n-1} - 11

Sequence Type Determination: We have the sequence: $1, 12, 23, 34, 45, 56, \ldots$ $\newline$ To determine the type of sequence, we need to check the difference between consecutive terms.
Calculate First Two Terms: Calculate the difference between the first two terms: $12 - 1 = 11$ .
Calculate Second and Third Terms: Calculate the difference between the second and third terms: $23 - 12 = 11$ .
Conclusion of Sequence Type: Since the difference between consecutive terms is constant, we can conclude that the sequence is an arithmetic sequence with a common difference of $11$ .
Arithmetic Sequence Recursive Formula: The recursive formula for an arithmetic sequence is given by $a_n = a_{n-1} + d$ , where $d$ is the common difference.
Substitute Common Difference: Substitute the common difference $11$ into the recursive formula to get the specific formula for this sequence: $a_n = a_{(n-1)} + 11$ .
Comparison with Choices: Comparing the derived formula with the given choices, we find that the correct choice is $(A)a_n = a_{(n-1)} + 11$ .