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Find the 12^th term of the geometric sequence
5,25,125,dots
Answer:

Find the $12^{\text {th }}$ term of the geometric sequence $5,25,125, \ldots$ $\newline$ Answer:

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Geometric sequences

Full solution

Q. Find the

12^{\text {th }}

term of the geometric sequence

5,25,125, \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 called the common 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. $\newline$ $\frac{25}{5} = 5$ $\newline$ Common Ratio $r$ : $5$
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 $12$ th term: Calculate the $12$ th term using the formula. $\newline$ First term $a_1 = 5$ $\newline$ Common Ratio $r = 5$ $\newline$ n = $12$ $\newline$ $a_{12} = 5 \times 5^{12-1} = 5 \times 5^{11}$
Perform exponentiation and multiplication: Perform the exponentiation and multiplication to find the $12^{\text{th}}$ term. $a_{12} = 5 \times 5^{11} = 5 \times 48828125$ $a_{12} = 244140625$

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