Find the 12th term of the geometric sequence shown below. 4x,-8x^(3),16x^(5),dots Answer:

Identify common ratio and formula: To find the 12th term of a geometric sequence, we need to identify the common ratio (r) and use the formula for the nth term of a geometric sequence, which is a_n = a_1 * r^(n-1), where a_1 is the first term and n is the term number.Find first term: The first term (a_1) of the sequence is 4x.Calculate common ratio: To find the common ratio (r), we divide the second term by the first term: r = (-8x^3) / (4x) = -2x^2.Find 12th term formula: Now that we have the common ratio, we can find the 12th term (a_12) using the formula: a_12 = a_1 * r^(12-1) = 4x * (-2x^2)^(11).Calculate exponent: We calculate the exponent: (-2x^2)^(11) = (-2)^11 * (x^2)^11 = -2048x^22.Multiply for 12th term: Now we multiply the first term by the result of the exponent calculation to get the 12th term: a_12 = 4x * -2048x^22 = -8192x^23.

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

4x,-8x^(3),16x^(5),dots
Answer:

Find the $12$ th term of the geometric sequence shown below. $\newline$ $4 x,-8 x^{3}, 16 x^{5}, \ldots$ $\newline$ Answer:

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Q. Find the

12

th term of the geometric sequence shown below.

\newline

4 x,-8 x^{3}, 16 x^{5}, \ldots

\newline

Answer:

Identify common ratio and formula: To find the $12^{\text{th}}$ term of a geometric sequence, we need to identify the common ratio ( $r$ ) and use the formula for the $n^{\text{th}}$ term of a geometric sequence, which is $a_n = a_1 \cdot r^{(n-1)}$ , where $a_1$ is the first term and $n$ is the term number.
Find first term: The first term $a_1$ of the sequence is $4x$ .
Calculate common ratio: To find the common ratio $r$ , we divide the second term by the first term: $r = \frac{-8x^3}{4x} = -2x^2$ .
Find $12$ th term formula: Now that we have the common ratio, we can find the $12$ th term $a_{12}$ using the formula: $a_{12} = a_1 \cdot r^{(12-1)} = 4x \cdot (-2x^2)^{11}$ .
Calculate exponent: We calculate the exponent: $(-2x^2)^{11} = (-2)^{11} \times (x^2)^{11} = -2048x^{22}.$
Multiply for $12$ th term: Now we multiply the first term by the result of the exponent calculation to get the $12$ th term: $a_{12} = 4x \times -2048x^{22} = -8192x^{23}$ .