Find the 8^th term of the geometric sequence 9,-27,81,dots Answer:

Identify Sequence Type: Identify the type of sequence and the common ratio. The sequence is geometric because each term is multiplied by a common ratio to get the next term. To find the common ratio, divide the second term by the first term. -27 / 9 = -3 Common Ratio: -3Find Common Ratio: Use the formula for the nth term of a geometric sequence. The nth term (a_n) of a geometric sequence can be found using the formula a_n = a_1 * r^(n-1), where a_1 is the first term, r is the common ratio, and n is the term number. For the 8th term, a_1 = 9, r = -3, and n = 8.Use nth Term Formula: Calculate the 8th term using the formula. a_8 = 9 * (-3)^(8-1) a_8 = 9 * (-3)^7 a_8 = 9 * (-2187) a_8 = -19683

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Find the 8^th term of the geometric sequence
9,-27,81,dots
Answer:

Find the $8^{\text {th }}$ term of the geometric sequence $9,-27,81, \ldots$ $\newline$ Answer:

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Q. Find the

8^{\text {th }}

term of the geometric sequence

9,-27,81, \ldots

\newline

Answer:

Identify Sequence Type: Identify the type of sequence and the common ratio. $\newline$ The sequence is geometric because each term is multiplied by a common ratio to get the next term. To find the common ratio, divide the second term by the first term. $\newline$ $-27 / 9 = -3$ $\newline$ Common Ratio: $-3$
Find Common Ratio: Use the formula for the nth term of a geometric sequence. $\newline$ The nth term $a_n$ of a geometric sequence can be found using the formula $a_n = a_1 \times r^{(n-1)}$ , where $a_1$ is the first term, $r$ is the common ratio, and $n$ is the term number. $\newline$ For the $8$ th term, $a_1 = 9$ , $r = -3$ , and $n = 8$ .
Use nth Term Formula: Calculate the $8$ th term using the formula. $\newline$ $a_8 = 9 \times (-3)^{8-1}$ $\newline$ $a_8 = 9 \times (-3)^7$ $\newline$ $a_8 = 9 \times (-2187)$ $\newline$ $a_8 = -19683$