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Find the
13^("th ") term of the arithmetic sequence
5x-6,-2x-11,-9x-16,dots
Answer:

Find the $13^{\text {th }}$ term of the arithmetic sequence $5 x-6,-2 x-11,-9 x-16, \ldots$ $\newline$ Answer:

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Find trigonometric functions using a calculator

Full solution

Q. Find the

13^{\text {th }}

term of the arithmetic sequence

5 x-6,-2 x-11,-9 x-16, \ldots

\newline

Answer:

Find Common Difference: To find the $13$ th term of an arithmetic sequence, we need to determine the common difference between consecutive terms and then use the formula for the $n$ th term of an arithmetic sequence, which is $a_n = a_1 + (n - 1)d$ , where $a_n$ is the $n$ th term, $a_1$ is the first term, and $d$ is the common difference.
Calculate $13$ th Term: First, let's find the common difference $d$ by subtracting the first term from the second term. $d = (-2x - 11) - (5x - 6)$ $d = -2x - 11 - 5x + 6$ $d = -7x - 5$
Simplify Expression: Now that we have the common difference, we can use the formula to find the $13^{\text{th}}$ term ( $a_{13}$ ). $\newline$ $a_{13} = a_1 + (13 - 1)d$ $\newline$ $a_{13} = (5x - 6) + 12(-7x - 5)$
Simplify Expression: Now that we have the common difference, we can use the formula to find the $13$ th term $a_{13}$ . $a_{13} = a_1 + (13 - 1)d$ $a_{13} = (5x - 6) + 12(-7x - 5)$ Let's simplify the expression for $a_{13}$ . $a_{13} = 5x - 6 + 12(-7x) + 12(-5)$ $a_{13} = 5x - 6 - 84x - 60$ $a_{13} = -79x - 66$

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