Find the 10^th term of the geometric sequence 9,45,225,dots Answer:

Identify Sequence Type: Identify the type of sequence. The given sequence is geometric because each term after the first is obtained by multiplying the previous term by a constant ratio.Determine Common Ratio: Determine the common ratio (r) of the sequence. To find the common ratio, divide the second term by the first term. r = 45 / 9 = 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 = 9 * 5^(10-1) a_10 = 9 * 5^9Perform Exponentiation: Perform the exponentiation. 5^9 = 1953125Multiply by First Term: Multiply the result by the first term. a_10 = 9 * 1953125 a_10 = 17578125

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Find the 10^th term of the geometric sequence
9,45,225,dots
Answer:

Find the $10^{\text {th }}$ term of the geometric sequence $9,45,225, \ldots$ $\newline$ Answer:

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Q. Find the

10^{\text {th }}

term of the geometric sequence

9,45,225, \ldots

\newline

Answer:

Identify Sequence Type: Identify the type of sequence. The given sequence is geometric because each term after the first is obtained by multiplying the previous term by a constant 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. $\newline$ $r = \frac{45}{9} = 5$
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 $a_n = a_1 \cdot r^{(n-1)}$ , 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. $\newline$ $a_{10} = 9 \times 5^{10-1}$ $\newline$ $a_{10} = 9 \times 5^9$
Perform Exponentiation: Perform the exponentiation. $\newline$ $5^9 = 1953125$
Multiply by First Term: Multiply the result by the first term. $\newline$ $a_{10} = 9 \times 1953125$ $\newline$ $a_{10} = 17578125$