Find the 11^th term of the geometric sequence 1,2,4,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. The second term is 2 and the first term is 1. To find the common ratio, divide the second term by the first term. r = 2 / 1 = 2Use Formula for nth Term: Use the formula for the nth term of a geometric sequence to find the 11th term. The nth term of a geometric sequence is given by a_n = a_1 * r^(n-1), where a_1 is the first term and r is the common ratio.Plug Values for 11th Term: Plug the values into the formula to find the 11th term. a_11 = 1 * 2^(11-1) a_11 = 1 * 2^10Calculate 2^10: Calculate the value of 2^10. 2^10 = 1024Conclude Final Answer: Conclude the final answer. The 11th term of the geometric sequence is 1024.

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Find the 11^th term of the geometric sequence
1,2,4,dots
Answer:

Find the $11^{\text {th }}$ term of the geometric sequence $1,2,4, \ldots$ $\newline$ Answer:

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Q. Find the

11^{\text {th }}

term of the geometric sequence

1,2,4, \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. $\newline$ The second term is $2$ and the first term is $1$ . To find the common ratio, divide the second term by the first term. $\newline$ $r = \frac{2}{1} = 2$
Use Formula for nth Term: Use the formula for the nth term of a geometric sequence to find the $11^{th}$ term. $\newline$ The nth term of a geometric sequence is given by $a_n = a_1 \cdot r^{(n-1)}$ , where $a_1$ is the first term and $r$ is the common ratio.
Plug Values for $11$ th Term: Plug the values into the formula to find the $11$ th term. $\newline$ $a_{11} = 1 \times 2^{11-1}$ $\newline$ $a_{11} = 1 \times 2^{10}$
Calculate $2^{10}$ : Calculate the value of $2^{10}$ . $\newline$ $2^{10} = 1024$
Conclude Final Answer: Conclude the final answer. $\newline$ The $11^{\text{th}}$ term of the geometric sequence is $1024$ .