Find the 13^("th ") term of the geometric sequence 8,16,32,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 we want to find.Find common ratio: First, we identify the first term (a_1) of the sequence, which is 8.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: r = 16 / 8 = 2.Calculate exponent: Now that we have the first term and the common ratio, we can find the 13th term (a_13) using the formula: a_13 = 8 * 2^(13-1).Calculate 2^12: We calculate the exponent: 2^(13-1) = 2^12.Multiply first term: Next, we calculate 2^12, which is 4096.Finally, we multiply the first term by 4096 to find the 13th term: a_13 = 8 * 4096 = 32768.

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Find the
13^("th ") term of the geometric sequence
8,16,32,dots
Answer:

Find the $13^{\text {th }}$ term of the geometric sequence $8,16,32, \ldots$ $\newline$ Answer:

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Q. Find the

13^{\text {th }}

term of the geometric sequence

8,16,32, \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 we want to find.
Find common ratio: First, we identify the first term $a_1$ of the sequence, which is $8$ .
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: $r = \frac{16}{8} = 2$ .
Calculate exponent: Now that we have the first term and the common ratio, we can find the $13^{\text{th}}$ term ( $a_{13}$ ) using the formula: $a_{13} = 8 \times 2^{(13-1)}$ .
Calculate $2^{12}$ : We calculate the exponent: $2^{13-1} = 2^{12}$ .
Multiply first term: Next, we calculate $2^{12}$ , which is $4096$ .
Multiply first term: Next, we calculate $2^{12}$ , which is $4096$ .Finally, we multiply the first term by $4096$ to find the $13$ th term: $a_{13} = 8 \times 4096 = 32768$ .