Find the 8th term of the geometric sequence shown below. -7x,-7x^(6),-7x^(11),dots Answer:

Find Common Ratio: Identify the common ratio of the geometric sequence. To find the common ratio (r), we divide the second term by the first term. r = (-7x^6) / (-7x) Simplify the expression by canceling out common factors. r = x^6 / x r = x^(6-1) r = x^5Use nth Term Formula: Use the formula for the nth term of a geometric sequence. The nth term (T_n) of a geometric sequence can be found using the formula T_n = a * r^(n-1), where a is the first term and r is the common ratio. Here, a = -7x and r = x^5. We want to find the 8th term, so n = 8.Substitute Values: Substitute the values into the formula to find the 8th term. T_8 = -7x * (x^5)^(8-1) T_8 = -7x * (x^5)^7Simplify 8th Term: Simplify the expression for the 8th term. T_8 = -7x * x^(5*7) T_8 = -7x * x^35 T_8 = -7x^(1+35) T_8 = -7x^36

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Find the 8th term of the geometric sequence shown below.

-7x,-7x^(6),-7x^(11),dots
Answer:

Find the $8$ th term of the geometric sequence shown below. $\newline$ $-7 x,-7 x^{6},-7 x^{11}, \ldots$ $\newline$ Answer:

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Algebra 1

Multiplication with rational exponents

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Q. Find the

8

th term of the geometric sequence shown below.

\newline

-7 x,-7 x^{6},-7 x^{11}, \ldots

\newline

Answer:

Find Common Ratio: Identify the common ratio of the geometric sequence. $\newline$ To find the common ratio $r$ , we divide the second term by the first term. $\newline$ $r = \frac{-7x^6}{-7x}$ $\newline$ Simplify the expression by canceling out common factors. $\newline$ $r = \frac{x^6}{x}$ $\newline$ $r = x^{6-1}$ $\newline$ $r = x^5$
Use nth Term Formula: Use the formula for the nth term of a geometric sequence. $\newline$ The nth term $T_n$ of a geometric sequence can be found using the formula $T_n = a \cdot r^{(n-1)}$ , where $a$ is the first term and $r$ is the common ratio. $\newline$ Here, $a = -7x$ and $r = x^5$ . We want to find the $8$ th term, so $n = 8$ .
Substitute Values: Substitute the values into the formula to find the $8^{\text{th}}$ term. $T_8 = -7x \times (x^5)^{8-1}$ $T_8 = -7x \times (x^5)^7$
Simplify $8$ th Term: Simplify the expression for the $8$ th term. $\newline$ $T_8 = -7x \times x^{5\times7}$ $\newline$ $T_8 = -7x \times x^{35}$ $\newline$ $T_8 = -7x^{1+35}$ $\newline$ $T_8 = -7x^{36}$