Find the 9th term of the geometric sequence shown below. -x^(5),-x^(9),-x^(13),dots Answer:

Identify Common Ratio: To find the 9th 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 = (-x^9) / (-x^5) = x^(9-5) = x^4Calculate 9th Term: Now that we have the common ratio (r = x^4), we can find the 9th term (a_9) 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_9 = (-x^5) * (x^4)^(9-1) = (-x^5) * (x^4)^8Simplify Exponent: Next, we simplify the expression for a_9 by calculating (x^4)^8. Calculation: (x^4)^8 = x^(4*8) = x^32Multiply to Find 9th Term: Now we can multiply the first term by x^32 to find the 9th term. Calculation: a_9 = (-x^5) * x^32 = -x^(5+32) = -x^37

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Find the 9th term of the geometric sequence shown below.

-x^(5),-x^(9),-x^(13),dots
Answer:

Find the $9$ th term of the geometric sequence shown below. $\newline$ $-x^{5},-x^{9},-x^{13}, \ldots$ $\newline$ Answer:

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Q. Find the

9

th term of the geometric sequence shown below.

\newline

-x^{5},-x^{9},-x^{13}, \ldots

\newline

Answer:

Identify Common Ratio: To find the $9$ 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: $r = (-x^9) / (-x^5) = x^{9-5} = x^4$
Calculate $9$ th Term: Now that we have the common ratio $r = x^4$ , we can find the $9$ th term $a_9$ 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: $a_9 = (-x^5) \cdot (x^4)^{9-1} = (-x^5) \cdot (x^4)^8$
Simplify Exponent: Next, we simplify the expression for $a_9$ by calculating $(x^4)^8$ . $\newline$ Calculation: $(x^4)^8 = x^{(4*8)} = x^{32}$
Multiply to Find $9$ th Term: Now we can multiply the first term by $x^{32}$ to find the $9$ th term. $\newline$ Calculation: $a_9 = (-x^5) \times x^{32} = -x^{5+32} = -x^{37}$