Find the 11th term of the arithmetic sequence x+1,-5x+7,-11 x+13,dots Answer:

Determine common difference: To find the 11th term of an arithmetic sequence, we need to determine the common difference between consecutive terms and then use the formula for the nth term of an arithmetic sequence, which is 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.Find common difference: First, let's find the common difference (d) by subtracting the first term from the second term. d = (-5x + 7) - (x + 1) = -5x + 7 - x - 1 = -6x + 6Verify common difference: Now, let's verify the common difference by subtracting the second term from the third term. d = (-11x + 13) - (-5x + 7) = -11x + 13 + 5x - 7 = -6x + 6 This confirms that the common difference is indeed -6x + 6.Find 11th term: Using the formula for the nth term, we can now find the 11th term (a_11). a_11 = a_1 + (11 - 1)(-6x + 6) = (x + 1) + 10(-6x + 6)Simplify expression: Simplify the expression to find the 11th term. a_11 = x + 1 + 10(-6x) + 10(6) = x + 1 - 60x + 60Combine like terms: Combine like terms to get the final expression for the 11th term. a_11 = -59x + 61

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Find the 11th term of the arithmetic sequence
x+1,-5x+7,-11 x+13,dots
Answer:

Find the $11$ th term of the arithmetic sequence $x+1,-5 x+7,-11 x+13, \ldots$ $\newline$ Answer:

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Q. Find the

11

th term of the arithmetic sequence

x+1,-5 x+7,-11 x+13, \ldots

\newline

Answer:

Determine common difference: To find the $11^{\text{th}}$ term of an arithmetic sequence, we need to determine the common difference between consecutive terms and then use the formula for the $n^{\text{th}}$ term of an arithmetic sequence, which is $a_n = a_1 + (n - 1)d$ , where $a_n$ is the $n^{\text{th}}$ term, $a_1$ is the first term, $n$ is the term number, and $d$ is the common difference.
Find common difference: First, let's find the common difference $d$ by subtracting the first term from the second term. $d = (-5x + 7) - (x + 1) = -5x + 7 - x - 1 = -6x + 6$
Verify common difference: Now, let's verify the common difference by subtracting the second term from the third term. $\newline$ $d = (-11x + 13) - (-5x + 7) = -11x + 13 + 5x - 7 = -6x + 6$ $\newline$ This confirms that the common difference is indeed $-6x + 6$ .
Find $11$ th term: Using the formula for the nth term, we can now find the $11$ th term $a_{11}$ . $a_{11} = a_1 + (11 - 1)(-6x + 6) = (x + 1) + 10(-6x + 6)$
Simplify expression: Simplify the expression to find the $11^{\text{th}}$ term. $a_{11} = x + 1 + 10(-6x) + 10(6) = x + 1 - 60x + 60$
Combine like terms: Combine like terms to get the final expression for the $11^{th}$ term. $a_{11} = -59x + 61$