Find the 10^("th ") term of the following geometric sequence. 3,15,75,375,dots

Find Common Ratio: Identify the common ratio (r) of the geometric sequence. To find the common ratio, we divide the second term by the first term. r = 15 / 3 = 5Use Formula for nth Term: Use the formula for the nth term of a geometric sequence. The nth term (a_n) of a geometric sequence can be found using the formula: a_n = a_1 * r^(n-1) where a_1 is the first term and r is the common ratio.Calculate 10th Term: Calculate the 10th term using the formula. a_10 = a_1 * r^(10-1) a_10 = 3 * 5^(10-1) a_10 = 3 * 5^9Perform Exponentiation: Perform the exponentiation. 5^9 = 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 * 5 5^9 = 1953125Multiply First Term: Multiply the first term by the result of the exponentiation. a_10 = 3 * 1953125 a_10 = 5859375

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Find the
10^("th ") term of the following geometric sequence.

3,15,75,375,dots

Find the $10^{\text {th }}$ term of the following geometric sequence. $\newline$ $3,15,75,375, \ldots$

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Algebra 2

Introduction to sigma notation

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Q. Find the

10^{\text {th }}

term of the following geometric sequence.

\newline

3,15,75,375, \ldots

Find Common Ratio: Identify the common ratio $r$ of the geometric sequence. $\newline$ To find the common ratio, we divide the second term by the first term. $\newline$ $r = \frac{15}{3} = 5$
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: $\newline$ $a_n = a_1 \cdot r^{(n-1)}$ $\newline$ where $a_1$ is the first term and $r$ is the common ratio.
Calculate $10$ th Term: Calculate the $10$ th term using the formula. $\newline$ $a_{10} = a_1 \times r^{10-1}$ $\newline$ $a_{10} = 3 \times 5^{10-1}$ $\newline$ $a_{10} = 3 \times 5^9$
Perform Exponentiation: Perform the exponentiation. $\newline$ $5^9 = 5 \times 5 \times 5 \times 5 \times 5 \times 5 \times 5 \times 5 \times 5$ $\newline$ $5^9 = 1953125$
Multiply First Term: Multiply the first term by the result of the exponentiation. $\newline$ $a_{10} = 3 \times 1953125$ $\newline$ $a_{10} = 5859375$