Find the 10^th term of the geometric sequence 5,-25,125,dots Answer:

Identify type and ratio: Identify the type of sequence and the common ratio. The given sequence is geometric because each term is multiplied by a common ratio to get the next term. To find the common ratio, divide the second term by the first term. Common Ratio (r) = -25 / 5 = -5Use nth term formula: 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. We want to find the 10th term (a_10), so n = 10.Substitute values: Substitute the values into the formula. a_10 = 5 * (-5)^(10-1) a_10 = 5 * (-5)^9Calculate 10th term: Calculate the 10th term. a_10 = 5 * (-5)^9 a_10 = 5 * (-1953125) a_10 = -9765625

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Find the 10^th term of the geometric sequence
5,-25,125,dots
Answer:

Find the $10^{\text {th }}$ term of the geometric sequence $5,-25,125, \ldots$ $\newline$ Answer:

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Q. Find the

10^{\text {th }}

term of the geometric sequence

5,-25,125, \ldots

\newline

Answer:

Identify type and ratio: Identify the type of sequence and the common ratio. $\newline$ The given sequence is geometric because each term is multiplied by a common ratio to get the next term. $\newline$ To find the common ratio, divide the second term by the first term. $\newline$ Common Ratio $r$ = $-25 / 5 = -5$
Use nth term formula: 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. $\newline$ We want to find the $10$ th term $a_{10}$ , so $n = 10$ .
Substitute values: Substitute the values into the formula. $\newline$ $a_{10} = 5 \times (-5)^{10-1}$ $\newline$ $a_{10} = 5 \times (-5)^9$
Calculate $10$ th term: Calculate the $10$ th term. $\newline$ $a_{10} = 5 \times (-5)^9$ $\newline$ $a_{10} = 5 \times (-1953125)$ $\newline$ $a_{10} = -9765625$