Find the 9^th term of the geometric sequence 2,6,18,dots Answer:

Identify Sequence Type: Identify the type of sequence. The given sequence is geometric because each term after the first is found by multiplying the previous term by a constant called the common ratio.Determine Common Ratio: Determine the common ratio (r) of the sequence. To find the common ratio, divide the second term by the first term. r = 6 / 2 = 3Use Formula for nth Term: 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 and r is the common ratio.Calculate 9th Term: Calculate the 9th term using the formula. a_9 = a_1 * r^(9-1) a_9 = 2 * 3^(9-1) a_9 = 2 * 3^8Perform Exponentiation: Perform the exponentiation. 3^8 = 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 = 6561Multiply First Term: Multiply the first term by the result of the exponentiation to get the 9th term. a_9 = 2 * 6561 a_9 = 13122

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Find the 9^th term of the geometric sequence
2,6,18,dots
Answer:

Find the $9^{\text {th }}$ term of the geometric sequence $2,6,18, \ldots$ $\newline$ Answer:

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Q. Find the

9^{\text {th }}

term of the geometric sequence

2,6,18, \ldots

\newline

Answer:

Identify Sequence Type: Identify the type of sequence. The given sequence is geometric because each term after the first is found by multiplying the previous term by a constant called the common ratio.
Determine Common Ratio: Determine the common ratio $r$ of the sequence. $\newline$ To find the common ratio, divide the second term by the first term. $\newline$ $r = \frac{6}{2} = 3$
Use Formula for nth Term: 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 $a_n = a_1 \cdot r^{(n-1)}$ , where $a_1$ is the first term and $r$ is the common ratio.
Calculate $9$ th Term: Calculate the $9$ th term using the formula. $\newline$ $a_9 = a_1 \cdot r^{9-1}$ $\newline$ $a_9 = 2 \cdot 3^{9-1}$ $\newline$ $a_9 = 2 \cdot 3^8$
Perform Exponentiation: Perform the exponentiation. $3^8 = 3 \times 3 \times 3 \times 3 \times 3 \times 3 \times 3 \times 3 = 6561$
Multiply First Term: Multiply the first term by the result of the exponentiation to get the $9^{\text{th}}$ term. $\newline$ $a_9 = 2 \times 6561$ $\newline$ $a_9 = 13122$