Find the 9th term of the geometric sequence shown below. -4x^(6),4x^(11),-4x^(16),dots Answer:

Identify common ratio: To find the 9th 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 = (4x^(11)) / (-4x^(6)) = -x^(5)Find 9th term formula: Now that we have the common ratio, we can find the 9th term (a_9) using the formula for the nth term of a geometric sequence: a_n = a_1 * r^(n-1), where a_1 is the first term and n is the term number.Substitute values in formula: The first term (a_1) is -4x^(6). We want to find the 9th term (a_9), so we plug in the values into the formula: a_9 = (-4x^(6)) * (-x^(5))^(9-1)Simplify exponent: Simplify the exponent in the formula: a_9 = (-4x^(6)) * (-x^(5))^(8)Calculate power: Now, we calculate the power of -x^(5) raised to the 8th power: (-x^(5))^8 = x^(5*8) = x^(40) Since the base is negative and the exponent is even, the result will be positive.Multiply terms: Multiply the first term by the result we just found: a_9 = (-4x^(6)) * x^(40)Combine like terms: Combine the like terms by adding the exponents: a_9 = -4x^(6+40) = -4x^(46)

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Find the 9th term of the geometric sequence shown below.

-4x^(6),4x^(11),-4x^(16),dots
Answer:

Find the $9$ th term of the geometric sequence shown below. $\newline$ $-4 x^{6}, 4 x^{11},-4 x^{16}, \ldots$ $\newline$ Answer:

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Q. Find the

9

th term of the geometric sequence shown below.

\newline

-4 x^{6}, 4 x^{11},-4 x^{16}, \ldots

\newline

Answer:

Identify common ratio: To find the $9^{th}$ 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: $r = \frac{4x^{11}}{-4x^{6}} = -x^{5}$
Find $9$ th term formula: Now that we have the common ratio, we can find the $9$ th term $a_9$ using the formula for the nth term of a geometric sequence: $a_n = a_1 \cdot r^{(n-1)}$ , where $a_1$ is the first term and $n$ is the term number.
Substitute values in formula: The first term $a_1$ is $-4x^{6}$ . We want to find the $9$ th term $a_9$ , so we plug in the values into the formula: $\newline$ $a_9 = (-4x^{6}) \cdot (-x^{5})^{9-1}$
Simplify exponent: Simplify the exponent in the formula: $a_9 = (-4x^{6}) \cdot (-x^{5})^{8}$
Calculate power: Now, we calculate the power of $-x^{5}$ raised to the $8$ th power: $\newline$ $(-x^{5})^8 = x^{5*8} = x^{40}$ $\newline$ Since the base is negative and the exponent is even, the result will be positive.
Multiply terms: Multiply the first term by the result we just found: $a_9 = (-4x^{6}) \times x^{40}$
Combine like terms: Combine the like terms by adding the exponents: $a_9 = -4x^{(6+40)} = -4x^{46}$