Find the 8^th term of the geometric sequence 2,6,18,dots Answer:

Identify type of sequence: 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 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 8th term: Calculate the 8th term using the formula. a_8 = 2 * 3^(8-1) = 2 * 3^7Perform exponentiation: Perform the exponentiation. 3^7 = 3 * 3 * 3 * 3 * 3 * 3 * 3 = 2187Multiply by first term: Multiply the result by the first term. a_8 = 2 * 2187 = 4374

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Find the 8^th term of the geometric sequence
2,6,18,dots
Answer:

Find the $8^{\text {th }}$ term of the geometric sequence $2,6,18, \ldots$ $\newline$ Answer:

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Q. Find the

8^{\text {th }}

term of the geometric sequence

2,6,18, \ldots

\newline

Answer:

Identify type of sequence: Identify the type of sequence. $\newline$ The given sequence is geometric because each term after the first is found by multiplying the previous term by a constant 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 $a_n = a_1 \times r^{(n-1)}$ , where $a_1$ is the first term and $r$ is the common ratio.
Calculate $8$ th term: Calculate the $8$ th term using the formula. $a_8 = 2 \times 3^{8-1} = 2 \times 3^7$
Perform exponentiation: Perform the exponentiation. $3^7 = 3 \times 3 \times 3 \times 3 \times 3 \times 3 \times 3 = 2187$
Multiply by first term: Multiply the result by the first term. $\newline$ $a_8 = 2 \times 2187 = 4374$