Find the 9^th term of the geometric sequence 1,-4,16,dots Answer:

Identify Common Ratio: To find the 9th term of a geometric sequence, we need to identify the common ratio (r) of the sequence. The common ratio is found by dividing any term by the previous term. Calculation: r = (-4) / 1 = -4Use Formula for nth Term: Now that we have the common ratio, we can use the formula for the nth term of a geometric sequence, which is a_n = a_1 * r^(n-1), where a_1 is the first term and n is the term number.Calculate for 9th Term: We are looking for the 9th term (n=9), and we know the first term (a_1) is 1, and the common ratio (r) is -4. Calculation: a_9 = 1 * (-4)^(9-1) = 1 * (-4)^8Calculate (-4)^8: Now we calculate (-4)^8. Since -4 is raised to an even power, the result will be positive. Calculation: (-4)^8 = 65536Multiply First Term: Finally, we multiply the first term by the result of (-4)^8 to find the 9th term. Calculation: a_9 = 1 * 65536 = 65536

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Find the 9^th term of the geometric sequence
1,-4,16,dots
Answer:

Find the $9^{\text {th }}$ term of the geometric sequence $1,-4,16, \ldots$ $\newline$ Answer:

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Q. Find the

9^{\text {th }}

term of the geometric sequence

1,-4,16, \ldots

\newline

Answer:

Identify Common Ratio: To find the $9^{\text{th}}$ term of a geometric sequence, we need to identify the common ratio ( $r$ ) of the sequence. The common ratio is found by dividing any term by the previous term. $\newline$ Calculation: $r = (-4) / 1 = -4$
Use Formula for nth Term: Now that we have the common ratio, we can use the formula for the nth term of a geometric sequence, which is $a_n = a_1 \times r^{(n-1)}$ , where $a_1$ is the first term and $n$ is the term number.
Calculate for $9$ th Term: We are looking for the $9$ th term $n=9$ , and we know the first term $a_1$ is $1$ , and the common ratio $r$ is $-4$ . $\newline$ Calculation: $a_9 = 1 \times (-4)^{9-1} = 1 \times (-4)^8$
Calculate $(-4)^8$ : Now we calculate $(-4)^8$ . Since $-4$ is raised to an even power, the result will be positive. $\newline$ Calculation: $(-4)^8 = 65536$
Multiply First Term: Finally, we multiply the first term by the result of $(-4)^8$ to find the $9$ th term. $\newline$ Calculation: $a_9 = 1 \times 65536 = 65536$