Find the 12th term of the geometric sequence shown below. 10x^(4),-10x^(7),10x^(10),dots Answer:

Find Common Ratio: Identify the common ratio (r) of the geometric sequence. The sequence is 10x^(4), -10x^(7), 10x^(10), ... To find the common ratio, divide the second term by the first term: r = (-10x^(7)) / (10x^(4)) = -x^(7-4) = -x^(3)Use Formula for nth Term: Use the formula for the nth term of a geometric sequence. The nth term (a_n) of a geometric sequence can be found using the formula: a_n = a_1 * r^(n-1) where a_1 is the first term and r is the common ratio.Calculate 12th Term: Calculate the 12th term using the formula. a_12 = 10x^(4) * (-x^(3))^(12-1) a_12 = 10x^(4) * (-x^(3))^(11)Simplify Expression: Simplify the expression for the 12th term. a_12 = 10x^(4) * (-1)^(11) * x^(3*11) a_12 = 10x^(4) * (-1) * x^(33) a_12 = -10x^(4+33) a_12 = -10x^(37)

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

10x^(4),-10x^(7),10x^(10),dots
Answer:

Find the $12$ th term of the geometric sequence shown below. $\newline$ $10 x^{4},-10 x^{7}, 10 x^{10}, \ldots$ $\newline$ Answer:

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Math Problems

Algebra 1

Identify a sequence as explicit or recursive

Full solution

Q. Find the

12

th term of the geometric sequence shown below.

\newline

10 x^{4},-10 x^{7}, 10 x^{10}, \ldots

\newline

Answer:

Find Common Ratio: Identify the common ratio $r$ of the geometric sequence. $\newline$ The sequence is $10x^{4}$ , $-10x^{7}$ , $10x^{10}$ , ... $\newline$ To find the common ratio, divide the second term by the first term: $\newline$ $r = \frac{-10x^{7}}{10x^{4}} = -x^{7-4} = -x^{3}$
Use Formula for nth Term: Use the formula for the nth term of a geometric sequence. $\newline$ The nth term $a_n$ of a geometric sequence can be found using the formula: $\newline$ $a_n = a_1 \cdot r^{(n-1)}$ $\newline$ where $a_1$ is the first term and $r$ is the common ratio.
Calculate $12$ th Term: Calculate the $12$ th term using the formula. $\newline$ $a_{12} = 10x^{4} \times (-x^{3})^{12-1}$ $\newline$ $a_{12} = 10x^{4} \times (-x^{3})^{11}$
Simplify Expression: Simplify the expression for the $12^{\text{th}}$ term. $\newline$ $a_{12} = 10x^{4} \times (-1)^{11} \times x^{3\times11}$ $\newline$ $a_{12} = 10x^{4} \times (-1) \times x^{33}$ $\newline$ $a_{12} = -10x^{4+33}$ $\newline$ $a_{12} = -10x^{37}$