Find the 14^("th ") term of the geometric sequence 5,10,20,dots Answer:

Identify first term: To find the 14th 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 5.Calculate 14th 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 = 10 / 5 = 2.Calculate 2^13: Now that we have the first term and the common ratio, we can find the 14th term (a_14) using the formula: a_14 = 5 * 2^(14-1) = 5 * 2^13.Multiply to get 14th term: Calculating 2^13: 2^13 = 8192.Now, we multiply the first term by 2^13 to get the 14th term: a_14 = 5 * 8192 = 40960.

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Find the
14^("th ") term of the geometric sequence
5,10,20,dots
Answer:

Find the $14^{\text {th }}$ term of the geometric sequence $5,10,20, \ldots$ $\newline$ Answer:

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Q. Find the

14^{\text {th }}

term of the geometric sequence

5,10,20, \ldots

\newline

Answer:

Identify first term: To find the $14^{th}$ term of a geometric sequence, we need to use the formula for the $n^{th}$ term of a geometric sequence, which is $a_n = a_1 \times r^{(n-1)}$ , where $a_1$ is the first term, $r$ is the common ratio, and $n$ is the term number.
Find common ratio: First, we identify the first term $a_1$ of the sequence, which is $5$ .
Calculate $14$ 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: $r = \frac{10}{5} = 2$ .
Calculate $2^{13}$ : Now that we have the first term and the common ratio, we can find the $14^{th}$ term ( $a_{14}$ ) using the formula: $a_{14} = 5 \times 2^{14-1} = 5 \times 2^{13}$ .
Multiply to get $14$ th term: Calculating $2^{13}$ : $2^{13} = 8192$ .
Multiply to get $14$ th term: Calculating $2^{13}$ : $2^{13} = 8192$ . Now, we multiply the first term by $2^{13}$ to get the $14$ th term: $a_{14} = 5 \times 8192 = 40960$ .