Find the 6th term of the arithmetic sequence 3x-9,x-15,-x-21,dots Answer:

Find Common Difference: To find the 6th term of the arithmetic sequence, we first need to determine the common difference (d) of the sequence. We can do this by subtracting the first term from the second term. Common difference (d) = (x - 15) - (3x - 9)Calculate Common Difference: Now, let's perform the subtraction to find the common difference. d = x - 15 - 3x + 9 d = -2x - 6Use Formula for nth Term: Next, we use the common difference to find the nth term of an arithmetic sequence using the formula: nth term = first term + (n - 1) * common difference We want to find the 6th term, so n = 6. 6th term = (3x - 9) + (6 - 1) * (-2x - 6)Simplify Expression: Now we simplify the expression to find the 6th term. 6th term = 3x - 9 + 5 * (-2x - 6) 6th term = 3x - 9 - 10x - 30Combine Like Terms: Combine like terms to get the final expression for the 6th term. 6th term = -7x - 39

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Find the 6th term of the arithmetic sequence
3x-9,x-15,-x-21,dots
Answer:

Find the $6$ th term of the arithmetic sequence $3 x-9, x-15,-x-21, \ldots$ $\newline$ Answer:

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Math Problems

Grade 7

Evaluate variable expressions for Sequences

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Q. Find the

6

th term of the arithmetic sequence

3 x-9, x-15,-x-21, \ldots

\newline

Answer:

Find Common Difference: To find the $6^{\text{th}}$ term of the arithmetic sequence, we first need to determine the common difference ( $d$ ) of the sequence. We can do this by subtracting the first term from the second term. $\newline$ Common difference ( $d$ ) = ( $x - 15$ ) - ( $3x - 9$ )
Calculate Common Difference: Now, let's perform the subtraction to find the common difference. $\newline$ $d = x - 15 - 3x + 9$ $\newline$ $d = -2x - 6$
Use Formula for nth Term: Next, we use the common difference to find the nth term of an arithmetic sequence using the formula: $\newline$ nth term = first term + $(n - 1) \times \text{common difference}$ $\newline$ We want to find the $6^{\text{th}}$ term, so $n = 6$ . $\newline$ $6^{\text{th}}$ term = $(3x - 9) + (6 - 1) \times (-2x - 6)$
Simplify Expression: Now we simplify the expression to find the $6^{\text{th}}$ term.6^{\text{th}}\) term = 3x - 9 + 5 \times (-2x - 6)6^{\text{th}}\) term = 3x - 9 - 10x - 30
Combine Like Terms: Combine like terms to get the final expression for the $6$ th term. $6^{\text{th}}$ term = $-7x - 39$