Find the 13^("th ") term of the geometric sequence 6,18,54,dots Answer:

Identify first term: To find the 13th term of a geometric sequence, we need to use the formula for the nth term of a geometric sequence, which is 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.Find common ratio: First, we identify the first term (a_1) of the sequence, which is 6.Calculate 13th term: Next, we need to find the common ratio (r). We can do this by dividing the second term by the first term, or the third term by the second term. Let's use the second term divided by the first term: r = 18 / 6 = 3.Calculate power of ratio: Now that we have the first term and the common ratio, we can find the 13th term (a_13) using the formula: a_13 = a_1 * r^(13-1) = 6 * 3^(12).Multiply to find term: We calculate 3^(12). 3^(12) = 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 = 531,441.Finally, we multiply the first term by 3^(12) to find the 13th term: a_13 = 6 * 531,441 = 3,188,646.

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Find the
13^("th ") term of the geometric sequence
6,18,54,dots
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Find the $13^{\text {th }}$ term of the geometric sequence $6,18,54, \ldots$ $\newline$ Answer:

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Q. Find the

13^{\text {th }}

term of the geometric sequence

6,18,54, \ldots

\newline

Answer:

Identify first term: To find the $13^{\text{th}}$ term of a geometric sequence, we need to use the formula for the $n^{\text{th}}$ term of a geometric sequence, which is $a_n = a_1 \cdot r^{(n-1)}$ , where $a_1$ is the first term, $r$ is the common ratio, and $n$ is the term number.
Find common ratio: First, we identify the first term $a_1$ of the sequence, which is $6$ .
Calculate $13$ th term: Next, we need to find the common ratio $r$ . We can do this by dividing the second term by the first term, or the third term by the second term. Let's use the second term divided by the first term: $r = \frac{18}{6} = 3$ .
Calculate power of ratio: Now that we have the first term and the common ratio, we can find the $13$ th term $a_{13}$ using the formula: $a_{13} = a_1 \times r^{(13-1)} = 6 \times 3^{12}$ .
Multiply to find term: We calculate $3^{12}$ . $3^{12} = 3 \times 3 \times 3 \times 3 \times 3 \times 3 \times 3 \times 3 \times 3 \times 3 \times 3 \times 3 = 531,441$ .
Multiply to find term: We calculate $3^{12}$ . $3^{12} = 3 \times 3 \times 3 \times 3 \times 3 \times 3 \times 3 \times 3 \times 3 \times 3 \times 3 \times 3 = 531,441$ .Finally, we multiply the first term by $3^{12}$ to find the $13$ th term: $a_{13} = 6 \times 531,441 = 3,188,646$ .