Find the 7th term of the geometric sequence shown below. -6x^(7),30x^(8),-150x^(9),dots Answer:

Identify first term and ratio: To find the 7th term of a geometric sequence, we need to identify the first term (a1) and the common ratio (r) of the sequence. The first term (a1) is given as -6x^(7).Calculate common ratio: Next, we find the common ratio (r) by dividing the second term by the first term. r = (30x^(8)) / (-6x^(7)) r = -5xUse nth term formula: Now that we have the first term and the common ratio, we can use the formula for the nth term of a geometric sequence, which is an = a1 * r^(n-1), where n is the term number. We want to find the 7th term, so n = 7.Substitute values for 7th term: Substitute the values into the formula to find the 7th term. a7 = (-6x^(7)) * (-5x)^(7-1) a7 = (-6x^(7)) * (-5x)^(6)Simplify expression for 7th term: Simplify the expression to find the 7th term. a7 = (-6x^(7)) * (15625x^(6)) // (-5)^6 = 15625 a7 = -93750x^(13) // Multiply the coefficients and add the exponents for x

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

-6x^(7),30x^(8),-150x^(9),dots
Answer:

Find the $7$ th term of the geometric sequence shown below. $\newline$ $-6 x^{7}, 30 x^{8},-150 x^{9}, \ldots$ $\newline$ Answer:

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Q. Find the

7

th term of the geometric sequence shown below.

\newline

-6 x^{7}, 30 x^{8},-150 x^{9}, \ldots

\newline

Answer:

Identify first term and ratio: To find the $7^{\text{th}}$ term of a geometric sequence, we need to identify the first term ( $a_1$ ) and the common ratio ( $r$ ) of the sequence. $\newline$ The first term ( $a_1$ ) is given as $-6x^{7}$ .
Calculate common ratio: Next, we find the common ratio $r$ by dividing the second term by the first term. $r = \frac{30x^{8}}{-6x^{7}}$ $r = -5x$
Use nth term formula: Now that we have the first term and the common ratio, we can use the formula for the nth term of a geometric sequence, which is $a_n = a_1 \times r^{(n-1)}$ , where $n$ is the term number. $\newline$ We want to find the $7$ th term, so $n = 7$ .
Substitute values for $7$ th term: Substitute the values into the formula to find the $7$ th term. $\newline$ $a_7 = (-6x^{7}) \times (-5x)^{7-1}$ $\newline$ $a_7 = (-6x^{7}) \times (-5x)^{6}$
Simplify expression for $7$ th term: Simplify the expression to find the $7$ th term. $\newline$ $a_7 = (-6x^{7}) \times (15625x^{6}) // (-5)^6 = 15625$ $\newline$ $a_7 = -93750x^{13}$ // Multiply the coefficients and add the exponents for $x$