Which recursive formula can be used to define this sequence for n > 1? 10, 13, 16, 19, 22, 25, ... Choices: (A)a = a + 3 (B)a = a + a - 3 (C)a = 13/10a (D)a = a - 3

Determine Sequence Type: Determine if the sequence is arithmetic or geometric. We need to check if the difference between consecutive terms is constant (which would make it an arithmetic sequence) or if the ratio between consecutive terms is constant (which would make it a geometric sequence). Looking at the sequence: 10, 13, 16, 19, 22, 25, ... The difference between consecutive terms is: 13 - 10 = 3 16 - 13 = 3 19 - 16 = 3 22 - 19 = 3 25 - 22 = 3 Since the difference is constant, the sequence is arithmetic.Find Common Difference: Find the common difference of the arithmetic sequence. The common difference (d) is the difference between any two consecutive terms. Using the first two terms: 13 - 10 = 3 Therefore, the common difference is 3.Identify Recursive Formula: Identify the recursive formula for the arithmetic sequence. For an arithmetic sequence, the recursive formula is generally of the form: a_n = a_(n-1) + d Where a_n is the nth term, a_(n-1) is the (n-1)th term, and d is the common difference. Since we have determined that d = 3, the recursive formula is: a_n = a_(n-1) + 3

Home

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

10, 13, 16, 19, 22, 25, \ldots

\newline

Choices:

\newline

(A)

a_{n} = a_{n-1} + 3

\newline

(B)

a_{n} = a_{n-1} + a_{n-2} - 3

\newline

(C)

a_{n} = \frac{13}{10}a_{n-1}

\newline

(D)

a_{n} = a_{n-1} - 3

Determine Sequence Type: Determine if the sequence is arithmetic or geometric. $\newline$ We need to check if the difference between consecutive terms is constant (which would make it an arithmetic sequence) or if the ratio between consecutive terms is constant (which would make it a geometric sequence). $\newline$ Looking at the sequence: $10, 13, 16, 19, 22, 25, \ldots$ $\newline$ The difference between consecutive terms is: $\newline$ $13 - 10 = 3$ $\newline$ $16 - 13 = 3$ $\newline$ $19 - 16 = 3$ $\newline$ $22 - 19 = 3$ $\newline$ $25 - 22 = 3$ $\newline$ Since the difference is constant, the sequence is arithmetic.
Find Common Difference: Find the common difference of the arithmetic sequence. $\newline$ The common difference $d$ is the difference between any two consecutive terms. $\newline$ Using the first two terms: $\newline$ $13 - 10 = 3$ $\newline$ Therefore, the common difference is $3$ .
Identify Recursive Formula: Identify the recursive formula for the arithmetic sequence. $\newline$ For an arithmetic sequence, the recursive formula is generally of the form: $\newline$ $a_n = a_{n-1} + d$ $\newline$ Where $a_n$ is the nth term, $a_{n-1}$ is the $(n-1)$ th term, and $d$ is the common difference. $\newline$ Since we have determined that $d = 3$ , the recursive formula is: $\newline$ $a_n = a_{n-1} + 3$