Find the 7th term of the geometric sequence shown below. -10x^(6),10x^(11),-10x^(16),dots Answer:

Find Common Ratio: To find the 7th term of a geometric sequence, we need to identify the common ratio (r) between consecutive terms. We can find the common ratio by dividing the second term by the first term. Calculation: r = (10x^(11)) / (-10x^(6)) Simplification: r = -x^(5)Calculate 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: a_n = a_1 * r^(n-1), where a_1 is the first term and n is the term number. Calculation: a_7 = (-10x^(6)) * (-x^(5))^(7-1) Simplification: a_7 = (-10x^(6)) * (-x^(5))^6Simplify Expression: Next, we simplify the expression for a_7 by raising the common ratio to the 6th power. Calculation: a_7 = (-10x^(6)) * (x^(30)) Simplification: a_7 = -10x^(6+30) Simplification: a_7 = -10x^(36)

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

-10x^(6),10x^(11),-10x^(16),dots
Answer:

Find the $7$ th term of the geometric sequence shown below. $\newline$ $-10 x^{6}, 10 x^{11},-10 x^{16}, \ldots$ $\newline$ Answer:

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Q. Find the

7

th term of the geometric sequence shown below.

\newline

-10 x^{6}, 10 x^{11},-10 x^{16}, \ldots

\newline

Answer:

Find Common Ratio: To find the $7^{\text{th}}$ term of a geometric sequence, we need to identify the common ratio ( $r$ ) between consecutive terms. We can find the common ratio by dividing the second term by the first term. $\newline$ Calculation: $r = \frac{10x^{11}}{-10x^{6}}$ $\newline$ Simplification: $r = -x^{5}$
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: $a_n = a_1 \cdot r^{(n-1)}$ , where $a_1$ is the first term and $n$ is the term number. $\newline$ Calculation: $a_7 = (-10x^{6}) \cdot (-x^{5})^{(7-1)}$ $\newline$ Simplification: $a_7 = (-10x^{6}) \cdot (-x^{5})^6$
Simplify Expression: Next, we simplify the expression for $a_7$ by raising the common ratio to the $6$ th power. $\newline$ Calculation: $a_7 = (-10x^{6}) \times (x^{30})$ $\newline$ Simplification: $a_7 = -10x^{6+30}$ $\newline$ Simplification: $a_7 = -10x^{36}$