Find the 9 th term of the arithmetic sequence 5x+8,-2x+13,-9x+18,dots Answer:

Define Common Difference: To find the 9th 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.Calculate Common Difference: First, let's find the common difference (d) by subtracting the first term from the second term. d = (-2x + 13) - (5x + 8) d = -2x + 13 - 5x - 8 d = -7x + 5Verify Consistency: Now, let's verify the common difference by subtracting the second term from the third term to ensure it is consistent. d = (-9x + 18) - (-2x + 13) d = -9x + 18 + 2x - 13 d = -7x + 5 Since we got the same common difference, we can confirm that the sequence is arithmetic and the common difference is correct.Find 9th Term: Next, we use the formula for the nth term of an arithmetic sequence to find the 9th term (a_9). a_9 = a_1 + (9 - 1)d a_9 = (5x + 8) + 8(-7x + 5)Simplify Expression: Now, let's simplify the expression for the 9th term. a_9 = 5x + 8 + 8(-7x) + 8(5) a_9 = 5x + 8 - 56x + 40 a_9 = -51x + 48

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Find the 9 th term of the arithmetic sequence
5x+8,-2x+13,-9x+18,dots
Answer:

Find the $9$ th term of the arithmetic sequence $5 x+8,-2 x+13,-9 x+18, \ldots$ $\newline$ Answer:

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Grade 8

Sequences: mixed review

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Q. Find the

9

th term of the arithmetic sequence

5 x+8,-2 x+13,-9 x+18, \ldots

\newline

Answer:

Define Common Difference: To find the $9^{th}$ 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, $n$ is the term number, 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. $\newline$ $d = (-2x + 13) - (5x + 8)$ $\newline$ $d = -2x + 13 - 5x - 8$ $\newline$ $d = -7x + 5$
Verify Consistency: Now, let's verify the common difference by subtracting the second term from the third term to ensure it is consistent. $\newline$ $d = (-9x + 18) - (-2x + 13)$ $\newline$ $d = -9x + 18 + 2x - 13$ $\newline$ $d = -7x + 5$ $\newline$ Since we got the same common difference, we can confirm that the sequence is arithmetic and the common difference is correct.
Find $9$ th Term: Next, we use the formula for the nth term of an arithmetic sequence to find the $9$ th term $a_9$ . $a_9 = a_1 + (9 - 1)d$ $a_9 = (5x + 8) + 8(-7x + 5)$
Simplify Expression: Now, let's simplify the expression for the $9^{\text{th}}$ term. $a_9 = 5x + 8 + 8(-7x) + 8(5)$ $a_9 = 5x + 8 - 56x + 40$ $a_9 = -51x + 48$