Which recursive formula can be used to define this sequence for n > 1? -4, 11, 26, 41, 56, 71, ... Choices: (A)a = a + 15 (B)a = a + a - 15 (C)a = -11/4a (D)a = 1/15a

Sequence Type Determination: We have the sequence: -4, 11, 26, 41, 56, 71, ... Is the given sequence geometric or arithmetic? The difference between consecutive terms appears to be constant. The given sequence is likely arithmetic.Calculation of Differences: To confirm that the sequence is arithmetic, we calculate the difference between consecutive terms. Difference between the first and second term: 11 - (-4) = 15 Difference between the second and third term: 26 - 11 = 15 Since the difference is the same, the sequence is indeed arithmetic with a common difference of 15.Recursive Formula Identification: Identify the recursive formula for the given arithmetic sequence. The common difference is 15, so the recursive formula will involve adding 15 to the previous term. The correct recursive formula is: a_n = a_(n-1) + 15Matching with Choices: Now, we match our recursive formula with the given choices. The correct choice that represents the recursive formula a_n = a_(n-1) + 15 is: (A) a = a + 15

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Which recursive formula can be used to define this sequence for n > 1? $\newline$ $-4, 11, 26, 41, 56, 71, \ldots$ $\newline$ Choices: $\newline$ (A) $a_{n} = a_{n-1} + 15$ $\newline$ (B) $a_{n} = a_{n-1} + a_{n-2} - 15$ $\newline$ (C) $a_{n} = -\frac{11}{4}a_{n-1}$ $\newline$ (D) $a_{n} = \frac{1}{15}a_{n-1}$

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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

-4, 11, 26, 41, 56, 71, \ldots

\newline

Choices:

\newline

(A)

a_{n} = a_{n-1} + 15

\newline

(B)

a_{n} = a_{n-1} + a_{n-2} - 15

\newline

(C)

a_{n} = -\frac{11}{4}a_{n-1}

\newline

(D)

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

Sequence Type Determination: We have the sequence: $-4, 11, 26, 41, 56, 71, ext{...}$ $\newline$ Is the given sequence geometric or arithmetic? $\newline$ The difference between consecutive terms appears to be constant. $\newline$ The given sequence is likely arithmetic.
Calculation of Differences: To confirm that the sequence is arithmetic, we calculate the difference between consecutive terms. $\newline$ Difference between the first and second term: $11 - (-4) = 15$ $\newline$ Difference between the second and third term: $26 - 11 = 15$ $\newline$ Since the difference is the same, the sequence is indeed arithmetic with a common difference of $15$ .
Recursive Formula Identification: Identify the recursive formula for the given arithmetic sequence. $\newline$ The common difference is $15$ , so the recursive formula will involve adding $15$ to the previous term. $\newline$ The correct recursive formula is: $a_n = a_{(n-1)} + 15$
Matching with Choices: Now, we match our recursive formula with the given choices. $\newline$ The correct choice that represents the recursive formula $a_n = a_{n-1} + 15$ is: $\newline$ (A) $a = a + 15$