Which recursive formula can be used to define this sequence for n > 1? 12, 22, 32, 42, 52, 62, ... Choices: (A)a = a + 10 (B)a = 11/6a (C)a = a + a + 10 (D)a = 10a

Sequence Type: We have the sequence: 12, 22, 32, 42, 52, 62, ... Is the given sequence geometric or arithmetic? The difference between consecutive terms is the same. The given sequence is arithmetic.Find Common Difference: Find the common difference, d. Two consecutive terms are 12 and 22. 22 - 12 = 10 Common difference (d): 10Recursive Formula: Identify the recursive formula for the given sequence. Substitute 10 for d in a_n = a_(n-1) + d. Recursive formula: a_n = a_(n-1) + 10

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Which recursive formula can be used to define this sequence for n > 1? $\newline$ $12, 22, 32, 42, 52, 62, \ldots$ $\newline$ Choices: $\newline$ (A) $a_{n} = a_{n-1} + 10$ $\newline$ (B) $a_{n} = \frac{11}{6}a_{n-1}$ $\newline$ (C) $a_{n} = a_{n-1} + a_{n-1} + 10$ $\newline$ (D) $a_{n} = 10a_{n-1}$

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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

12, 22, 32, 42, 52, 62, \ldots

\newline

Choices:

\newline

(A)

a_{n} = a_{n-1} + 10

\newline

(B)

a_{n} = \frac{11}{6}a_{n-1}

\newline

(C)

a_{n} = a_{n-1} + a_{n-1} + 10

\newline

(D)

a_{n} = 10a_{n-1}

Sequence Type: We have the sequence: $12, 22, 32, 42, 52, 62, \ldots$ $\newline$ Is the given sequence geometric or arithmetic? $\newline$ The difference between consecutive terms is the same. $\newline$ The given sequence is arithmetic.
Find Common Difference: Find the common difference, $d$ . $\newline$ Two consecutive terms are $12$ and $22$ . $\newline$ $22 - 12 = 10$ $\newline$ Common difference ( $d$ ): $10$
Recursive Formula: Identify the recursive formula for the given sequence. $\newline$ Substitute $10$ for $d$ in $a_n = a_{n-1} + d$ . $\newline$ Recursive formula: $a_n = a_{n-1} + 10$