Find the 9th term of the arithmetic sequence -2x-5,-5x-8,-8x-11,dots Answer:

Identify common difference: Identify the common difference in the arithmetic sequence. The sequence is given by -2x-5, -5x-8, -8x-11, ... To find the common difference, subtract the first term from the second term: (-5x-8) - (-2x-5) = -5x - 8 + 2x + 5 = -3x - 3 Subtract the second term from the third term: (-8x-11) - (-5x-8) = -8x - 11 + 5x + 8 = -3x - 3 The common difference is -3x - 3.Find nth term formula: Use the common difference to find the nth term formula. The nth term of an arithmetic sequence can be found using the formula: a_n = a_1 + (n - 1)d where a_n is the nth term, a_1 is the first term, n is the term number, and d is the common difference. Here, a_1 = -2x - 5 and d = -3x - 3.Substitute values for 9th term: Substitute the values into the nth term formula to find the 9th term. a_9 = a_1 + (9 - 1)d a_9 = (-2x - 5) + (8)(-3x - 3) a_9 = -2x - 5 - 24x - 24 a_9 = -26x - 29

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Find the 9th term of the arithmetic sequence
-2x-5,-5x-8,-8x-11,dots
Answer:

Find the $9$ th term of the arithmetic sequence $-2 x-5,-5 x-8,-8 x-11, \ldots$ $\newline$ Answer:

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Algebra 1

Identify a sequence as explicit or recursive

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Q. Find the

9

th term of the arithmetic sequence

-2 x-5,-5 x-8,-8 x-11, \ldots

\newline

Answer:

Identify common difference: Identify the common difference in the arithmetic sequence. $\newline$ The sequence is given by $-2x-5$ , $-5x-8$ , $-8x-11$ , ... $\newline$ To find the common difference, subtract the first term from the second term: $\newline$ $(-5x-8) - (-2x-5) = -5x - 8 + 2x + 5 = -3x - 3$ $\newline$ Subtract the second term from the third term: $\newline$ $(-8x-11) - (-5x-8) = -8x - 11 + 5x + 8 = -3x - 3$ $\newline$ The common difference is $-3x - 3$ .
Find nth term formula: Use the common difference to find the nth term formula. $\newline$ The nth term of an arithmetic sequence can be found using the formula: $\newline$ $a_n = a_1 + (n - 1)d$ $\newline$ where $a_n$ is the nth term, $a_1$ is the first term, $n$ is the term number, and $d$ is the common difference. $\newline$ Here, $a_1 = -2x - 5$ and $d = -3x - 3$ .
Substitute values for $9$ th term: Substitute the values into the nth term formula to find the $9$ th term. $\newline$ $a_9 = a_1 + (9 - 1)d$ $\newline$ $a_9 = (-2x - 5) + (8)(-3x - 3)$ $\newline$ $a_9 = -2x - 5 - 24x - 24$ $\newline$ $a_9 = -26x - 29$