Find the 8^th term of the geometric sequence 9,-18,36,dots Answer:

Find Common Ratio: To find the 8th term of the geometric sequence, we first need to determine the common ratio (r) of the sequence. The common ratio is found by dividing any term by the previous term. Calculation: r = (-18) / 9 = -2Calculate 8th Term: Now that we have the common ratio, we can find the nth term of a geometric sequence using the formula: a_n = a_1 * r^(n-1), where a_n is the nth term, a_1 is the first term, and r is the common ratio. Calculation: a_8 = 9 * (-2)^(8-1)Simplify Exponent: We simplify the exponent part of the formula: (-2)^(8-1) = (-2)^7. Calculation: (-2)^7 = -128Multiply First Term: Now we multiply the first term by the result from the previous step to find the 8th term. Calculation: a_8 = 9 * (-128) = -1152

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Find the 8^th term of the geometric sequence
9,-18,36,dots
Answer:

Find the $8^{\text {th }}$ term of the geometric sequence $9,-18,36, \ldots$ $\newline$ Answer:

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Q. Find the

8^{\text {th }}

term of the geometric sequence

9,-18,36, \ldots

\newline

Answer:

Find Common Ratio: To find the $8^{\text{th}}$ term of the geometric sequence, we first need to determine the common ratio ( $r$ ) of the sequence. The common ratio is found by dividing any term by the previous term. $\newline$ Calculation: $r = (-18) / 9 = -2$
Calculate $8$ th Term: Now that we have the common ratio, we can find the $n$ th term of a geometric sequence using the formula: $a_n = a_1 \cdot r^{(n-1)}$ , where $a_n$ is the $n$ th term, $a_1$ is the first term, and $r$ is the common ratio. $\newline$ Calculation: $a_8 = 9 \cdot (-2)^{8-1}$
Simplify Exponent: We simplify the exponent part of the formula: $(-2)^{(8-1)} = (-2)^7$ . $\newline$ Calculation: $(-2)^7 = -128$
Multiply First Term: Now we multiply the first term by the result from the previous step to find the $8^{\text{th}}$ term. $\newline$ Calculation: $a_8 = 9 \times (-128) = -1152$