Find the 10th term of the geometric sequence shown below. -3x^(6),6x^(10),-12x^(14),dots Answer:

Identify Common Ratio: To find the 10th term of a geometric sequence, we need to identify the common ratio (r) of the sequence. The common ratio is found by dividing any term by the previous term.Calculate Common Ratio: Let's find the common ratio by dividing the second term by the first term: r = (6x^(10)) / (-3x^(6)) = -2x^(4)Use Geometric Sequence Formula: 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 * r^(n-1), where a_1 is the first term and n is the term number.Determine First Term and Term Number: The first term a_1 is -3x^(6), the common ratio r is -2x^(4), and we want to find the 10th term (n=10).Plug Values into Formula: Plugging the values into the formula, we get: a_10 = a_1 * r^(10-1) = -3x^(6) * (-2x^(4))^(9)Calculate Exponentiation: Now we need to calculate (-2x^(4))^9. When we raise a power to a power, we multiply the exponents: (-2x^(4))^9 = (-2)^9 * (x^(4))^9 = -512 * x^(36)Calculate 10th Term: Substitute this back into the formula for the 10th term: a_10 = -3x^(6) * (-512 * x^(36)) = 1536 * x^(42)

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Find the 10th term of the geometric sequence shown below.

-3x^(6),6x^(10),-12x^(14),dots
Answer:

Find the $10$ th term of the geometric sequence shown below. $\newline$ $-3 x^{6}, 6 x^{10},-12 x^{14}, \ldots$ $\newline$ Answer:

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Q. Find the

10

th term of the geometric sequence shown below.

\newline

-3 x^{6}, 6 x^{10},-12 x^{14}, \ldots

\newline

Answer:

Identify Common Ratio: To find the $10$ th term of a geometric sequence, we need to identify the common ratio $(r)$ of the sequence. The common ratio is found by dividing any term by the previous term.
Calculate Common Ratio: Let's find the common ratio by dividing the second term by the first term: $r = \frac{6x^{10}}{-3x^{6}} = -2x^{4}$
Use Geometric Sequence Formula: Now that we have the common ratio, we can use the formula for the $n$ 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.
Determine First Term and Term Number: The first term $a_1$ is $-3x^{6}$ , the common ratio $r$ is $-2x^{4}$ , and we want to find the $10$ th term $(n=10)$ .
Plug Values into Formula: Plugging the values into the formula, we get: $\newline$ $a_{10} = a_1 \cdot r^{10-1} = -3x^{6} \cdot (-2x^{4})^{9}$
Calculate Exponentiation: Now we need to calculate $(-2x^{4})^{9}$ . When we raise a power to a power, we multiply the exponents: $\newline$ $(-2x^{4})^{9} = (-2)^{9} \times (x^{4})^{9} = -512 \times x^{36}$
Calculate $10$ th Term: Substitute this back into the formula for the $10$ th term: $\newline$ $a_{10} = -3x^{6} \times (-512 \times x^{36}) = 1536 \times x^{42}$