Find the 13^("th ") term of the arithmetic sequence x+1,-2x-3,-5x-7,dots Answer:

Identify First Term: To find the 13th term of an arithmetic sequence, we need to use the formula for the nth term of an arithmetic sequence, which is given by: \[ a_n = a_1 + (n - 1)d \] where $ a_n $ is the nth term, $ a_1 $ is the first term, $ n $ is the term number, and $ d $ is the common difference between the terms.Find Common Difference: First, we identify the first term $ a_1 $ of the sequence. The first term given is $ x + 1 $.Calculate 13th Term: Next, we need to find the common difference $ d $. The common difference is the difference between any two consecutive terms. We can find it by subtracting the first term from the second term: \[ d = (-2x - 3) - (x + 1) \] \[ d = -2x - 3 - x - 1 \] \[ d = -3x - 4 \]Now that we have the first term $ a_1 = x + 1 $ and the common difference $ d = -3x - 4 $, we can find the 13th term $ a_{13} $ using the formula: \[ a_{13} = a_1 + (13 - 1)d \] \[ a_{13} = (x + 1) + 12(-3x - 4) \] \[ a_{13} = x + 1 - 36x - 48 \] \[ a_{13} = -35x - 47 \]

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Find the
13^("th ") term of the arithmetic sequence
x+1,-2x-3,-5x-7,dots
Answer:

Find the $13^{\text {th }}$ term of the arithmetic sequence $x+1,-2 x-3,-5 x-7, \ldots$ $\newline$ Answer:

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Q. Find the

13^{\text {th }}

term of the arithmetic sequence

x+1,-2 x-3,-5 x-7, \ldots

\newline

Answer:

Identify First Term: To find the $13$ th term of an arithmetic sequence, we need to use the formula for the nth term of an arithmetic sequence, which is given by: $\newline$ $a_n = a_1 + (n - 1)d$ $\newline$ where $a_n$ is the nth term, $a_1$ is the first term, $n$ is the term number, and $d$ is the common difference between the terms.
Find Common Difference: First, we identify the first term $a_1$ of the sequence. The first term given is $x + 1$ .
Calculate $13$ th Term: Next, we need to find the common difference $d$ . The common difference is the difference between any two consecutive terms. We can find it by subtracting the first term from the second term: $\newline$ $d = (-2x - 3) - (x + 1)$ $\newline$ $d = -2x - 3 - x - 1$ $\newline$ $d = -3x - 4$
Calculate $13$ th Term: Next, we need to find the common difference $d$ . The common difference is the difference between any two consecutive terms. We can find it by subtracting the first term from the second term: $\newline$ $d = (-2x - 3) - (x + 1)$ $\newline$ $d = -2x - 3 - x - 1$ $\newline$ $d = -3x - 4$ Now that we have the first term $a_1 = x + 1$ and the common difference $d = -3x - 4$ , we can find the $13$ th term $a_{13}$ using the formula: $\newline$ $a_{13} = a_1 + (13 - 1)d$ $\newline$ $a_{13} = (x + 1) + 12(-3x - 4)$ $\newline$ $a_{13} = x + 1 - 36x - 48$ $\newline$ $a_{13} = -35x - 47$