Find the 11th term of the geometric sequence shown below. -3x^(2),9x^(6),-27x^(10),dots Answer:

Identify terms and ratio: Identify the first term (a1) and the common ratio (r) of the geometric sequence. The first term a1 is given as -3x^2. To find the common ratio r, we divide the second term by the first term. r = (9x^6) / (-3x^2) = -3x^(6-2) = -3x^4Find 11th term formula: Use the formula for the nth term of a geometric sequence to find the 11th term. The nth term an of a geometric sequence is given by an = a1 * r^(n-1). We want to find the 11th term, so n = 11. a11 = a1 * r^(11-1) = a1 * r^10Substitute and calculate: Substitute the values of a1 and r into the formula to calculate the 11th term. a11 = (-3x^2) * (-3x^4)^10 a11 = (-3x^2) * (-3)^10 * (x^4)^10 a11 = (-3x^2) * (59049) * (x^40)Simplify for 11th term: Simplify the expression to find the 11th term. a11 = (-3) * 59049 * x^(2+40) a11 = (-3) * 59049 * x^42 a11 = -177147 * x^42

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Find the 11th term of the geometric sequence shown below.

-3x^(2),9x^(6),-27x^(10),dots
Answer:

Find the $11$ th term of the geometric sequence shown below. $\newline$ $-3 x^{2}, 9 x^{6},-27 x^{10}, \ldots$ $\newline$ Answer:

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Math Problems

Algebra 1

Write variable expressions for arithmetic sequences

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Q. Find the

11

th term of the geometric sequence shown below.

\newline

-3 x^{2}, 9 x^{6},-27 x^{10}, \ldots

\newline

Answer:

Identify terms and ratio: Identify the first term $a_1$ and the common ratio $r$ of the geometric sequence. $\newline$ The first term $a_1$ is given as $-3x^2$ . $\newline$ To find the common ratio $r$ , we divide the second term by the first term. $\newline$ $r = \frac{9x^6}{-3x^2} = -3x^{6-2} = -3x^4$
Find $11$ th term formula: Use the formula for the $n$ th term of a geometric sequence to find the $11$ th term. $\newline$ The $n$ th term $a_n$ of a geometric sequence is given by $a_n = a_1 \cdot r^{(n-1)}$ . $\newline$ We want to find the $11$ th term, so $n = 11$ . $\newline$ $a_{11} = a_1 \cdot r^{(11-1)} = a_1 \cdot r^{10}$
Substitute and calculate: Substitute the values of $a_1$ and $r$ into the formula to calculate the $11$ th term. $a_{11} = (-3x^2) \cdot (-3x^4)^{10}$ $a_{11} = (-3x^2) \cdot (-3)^{10} \cdot (x^4)^{10}$ $a_{11} = (-3x^2) \cdot (59049) \cdot (x^{40})$
Simplify for $11$ th term: Simplify the expression to find the $11$ th term. $\newline$ $a_{11} = (-3) \times 59049 \times x^{(2+40)}$ $\newline$ $a_{11} = (-3) \times 59049 \times x^{42}$ $\newline$ $a_{11} = -177147 \times x^{42}$