Find the 7th term of the geometric sequence shown below. x^(4),-3x^(7),9x^(10),dots Answer:

Find Common Ratio: To find the 7th term of the geometric sequence, we first need to determine the common ratio (r) of the sequence. The common ratio can be found by dividing any term by the previous term. Let's divide the second term by the first term to find the common ratio. r = (-3x^7) / (x^4) r = -3x^(7-4) r = -3x^3Calculate 7th Term: Now that we have the common ratio, we can find the 7th term (a_7) using 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. The first term (a_1) is x^4, the common ratio (r) is -3x^3, and we want to find the 7th term (n=7). a_7 = x^4 * (-3x^3)^(7-1) a_7 = x^4 * (-3x^3)^6Simplify Expression: Now we need to simplify the expression for the 7th term. a_7 = x^4 * (-3)^6 * (x^3)^6 a_7 = x^4 * 729 * x^18 a_7 = 729 * x^(4+18) a_7 = 729 * x^22

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Find the 7th term of the geometric sequence shown below.

x^(4),-3x^(7),9x^(10),dots
Answer:

Find the $7$ th term of the geometric sequence shown below. $\newline$ $x^{4},-3 x^{7}, 9 x^{10}, \ldots$ $\newline$ Answer:

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Q. Find the

7

th term of the geometric sequence shown below.

\newline

x^{4},-3 x^{7}, 9 x^{10}, \ldots

\newline

Answer:

Find Common Ratio: To find the $7^{\text{th}}$ term of the geometric sequence, we first need to determine the common ratio ( $r$ ) of the sequence. The common ratio can be found by dividing any term by the previous term. $\newline$ Let's divide the second term by the first term to find the common ratio. $\newline$ $r = \frac{-3x^7}{x^4}$ $\newline$ $r = -3x^{7-4}$ $\newline$ $r = -3x^3$
Calculate $7$ th Term: Now that we have the common ratio, we can find the $7$ th term $a_7$ using the formula for the nth 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. $\newline$ The first term $a_1$ is $x^4$ , the common ratio $r$ is $-3x^3$ , and we want to find the $7$ th term $n=7$ . $\newline$ $a_7 = x^4 \cdot (-3x^3)^{(7-1)}$ $\newline$ $a_n = a_1 \cdot r^{(n-1)}$ $0$
Simplify Expression: Now we need to simplify the expression for the $7$ th term. $\newline$ $a_7 = x^4 \cdot (-3)^6 \cdot (x^3)^6$ $\newline$ $a_7 = x^4 \cdot 729 \cdot x^{18}$ $\newline$ $a_7 = 729 \cdot x^{4+18}$ $\newline$ $a_7 = 729 \cdot x^{22}$