Find the 12th term of the geometric sequence shown below. -x^(8),-2x^(9),-4x^(10),dots Answer:

Identify first term and common ratio: To find the 12th term of a geometric sequence, we need to identify the first term (a1) and the common ratio (r) of the sequence. The first term (a1) is given as -x^(8). The second term is -2x^(9), and the third term is -4x^(10). To find the common ratio (r), we divide the second term by the first term. r = (-2x^(9)) / (-x^(8)) = 2xCalculate common ratio: Now that we have the common ratio, we can use the formula for the nth term of a geometric sequence, which is an = a1 * r^(n-1), where an is the nth term. We want to find the 12th term (a12), so we substitute n = 12 into the formula. a12 = (-x^(8)) * (2x)^(12-1)Use formula for 12th term: Simplify the expression for the 12th term by calculating the exponent and multiplication. a12 = (-x^(8)) * (2x)^(11) a12 = (-x^(8)) * (2^11 * x^(11)) a12 = (-1) * (2^11) * x^(8+11) a12 = -2048 * x^(19)

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Find the 12th term of the geometric sequence shown below.

-x^(8),-2x^(9),-4x^(10),dots
Answer:

Find the $12$ th term of the geometric sequence shown below. $\newline$ $-x^{8},-2 x^{9},-4 x^{10}, \ldots$ $\newline$ Answer:

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Q. Find the

12

th term of the geometric sequence shown below.

\newline

-x^{8},-2 x^{9},-4 x^{10}, \ldots

\newline

Answer:

Identify first term and common ratio: To find the $12^{\text{th}}$ term of a geometric sequence, we need to identify the first term ( $a_1$ ) and the common ratio ( $r$ ) of the sequence. $\newline$ The first term ( $a_1$ ) is given as $-x^{8}$ . $\newline$ The second term is $-2x^{9}$ , and the third term is $-4x^{10}$ . $\newline$ To find the common ratio ( $r$ ), we divide the second term by the first term. $\newline$ $r = \frac{-2x^{9}}{-x^{8}} = 2x$
Calculate common ratio: Now that we have the common ratio, we can use the formula for the nth term of a geometric sequence, which is $a_n = a_1 \cdot r^{(n-1)}$ , where $a_n$ is the nth term. $\newline$ We want to find the $12$ th term ( $a_{12}$ ), so we substitute $n = 12$ into the formula. $\newline$ $a_{12} = (-x^{8}) \cdot (2x)^{12-1}$
Use formula for $12$ th term: Simplify the expression for the $12$ th term by calculating the exponent and multiplication. $\newline$ $a_{12} = (-x^{8}) \cdot (2x)^{11}$ $\newline$ $a_{12} = (-x^{8}) \cdot (2^{11} \cdot x^{11})$ $\newline$ $a_{12} = (-1) \cdot (2^{11}) \cdot x^{(8+11)}$ $\newline$ $a_{12} = -2048 \cdot x^{19}$