Find the 7 th term of the arithmetic sequence 5x-4,-2x-9,-9x-14,dots Answer:

Find Common Difference: To find the 7th 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, and d is the common difference.Calculate Common Difference: First, let's find the common difference (d) by subtracting the first term from the second term. d = (-2x - 9) - (5x - 4) d = -2x - 9 - 5x + 4 d = -7x - 5Use Formula for 7th Term: Now, let's verify the common difference by subtracting the second term from the third term. d = (-9x - 14) - (-2x - 9) d = -9x - 14 + 2x + 9 d = -7x - 5 This confirms that the common difference is indeed -7x - 5.Simplify 7th Term Expression: Using the formula for the nth term, we can now find the 7th term (a_7). a_7 = a_1 + (7 - 1)(-7x - 5) a_7 = (5x - 4) + 6(-7x - 5)Let's simplify the expression for the 7th term. a_7 = 5x - 4 + 6(-7x) + 6(-5) a_7 = 5x - 4 - 42x - 30 a_7 = -37x - 34

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Find the 7 th term of the arithmetic sequence
5x-4,-2x-9,-9x-14,dots
Answer:

Find the $7$ th term of the arithmetic sequence $5 x-4,-2 x-9,-9 x-14, \ldots$ $\newline$ Answer:

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Q. Find the

7

th term of the arithmetic sequence

5 x-4,-2 x-9,-9 x-14, \ldots

\newline

Answer:

Find Common Difference: To find the $7$ 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 Common Difference: First, let's find the common difference $d$ by subtracting the first term from the second term. $d = (-2x - 9) - (5x - 4)$ $d = -2x - 9 - 5x + 4$ $d = -7x - 5$
Use Formula for $7$ th Term: Now, let's verify the common difference by subtracting the second term from the third term. $\newline$ $d = (-9x - 14) - (-2x - 9)$ $\newline$ $d = -9x - 14 + 2x + 9$ $\newline$ $d = -7x - 5$ $\newline$ This confirms that the common difference is indeed $-7x - 5$ .
Simplify $7$ th Term Expression: Using the formula for the nth term, we can now find the $7$ th term $a_7$ . $a_7 = a_1 + (7 - 1)(-7x - 5)$ $a_7 = (5x - 4) + 6(-7x - 5)$
Simplify $7$ th Term Expression: Using the formula for the nth term, we can now find the $7$ th term $a_7$ . $a_7 = a_1 + (7 - 1)(-7x - 5)$ $a_7 = (5x - 4) + 6(-7x - 5)$ Let's simplify the expression for the $7$ th term. $a_7 = 5x - 4 + 6(-7x) + 6(-5)$ $a_7 = 5x - 4 - 42x - 30$ $a_7 = -37x - 34$