Find the 8th term of the geometric sequence shown below. -4x^(6),-20x^(8),-100x^(10),dots Answer:

Identify Common Ratio: To find the 8th term of a geometric sequence, we need to identify the common ratio (r) of the sequence. The common ratio can be found by dividing any term by the previous term.Calculate Common Ratio: Let's find the common ratio by dividing the second term by the first term: r = (-20x^8) / (-4x^6) = 5x^2Find 8th Term: Now that we have the common ratio, we can find the 8th term (a_8) using the formula for the nth term of a geometric sequence: a_n = a_1 * r^(n-1) where a_1 is the first term and n is the term number.Substitute Values: Substitute the known values into the formula to find the 8th term: a_8 = (-4x^6) * (5x^2)^(8-1) a_8 = (-4x^6) * (5x^2)^7Calculate 8th Term: Calculate the 8th term: a_8 = (-4x^6) * (5^7 * x^(2*7)) a_8 = (-4x^6) * (78125 * x^14)Multiply Terms: Multiply the terms together: a_8 = -4 * 78125 * x^(6+14) a_8 = -312500 * x^20

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Find the 8th term of the geometric sequence shown below.

-4x^(6),-20x^(8),-100x^(10),dots
Answer:

Find the $8$ th term of the geometric sequence shown below. $\newline$ $-4 x^{6},-20 x^{8},-100 x^{10}, \ldots$ $\newline$ Answer:

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Q. Find the

8

th term of the geometric sequence shown below.

\newline

-4 x^{6},-20 x^{8},-100 x^{10}, \ldots

\newline

Answer:

Identify Common Ratio: To find the $8^{\text{th}}$ term of a geometric sequence, we need to identify the common ratio ( $r$ ) of the sequence. The common ratio can be found by dividing any term by the previous term.
Calculate Common Ratio: Let's find the common ratio by dividing the second term by the first term: $r = \frac{-20x^8}{-4x^6} = 5x^2$
Find $8$ th Term: Now that we have the common ratio, we can find the $8$ th term $a_8$ using the formula for the nth term of a geometric sequence: $\newline$ $a_n = a_1 \cdot r^{(n-1)}$ $\newline$ where $a_1$ is the first term and $n$ is the term number.
Substitute Values: Substitute the known values into the formula to find the $8^{\text{th}}$ term: $\newline$ $a_8 = (-4x^6) \times (5x^2)^{8-1}$ $\newline$ $a_8 = (-4x^6) \times (5x^2)^7$
Calculate $8$ th Term: Calculate the $8$ th term: $\newline$ $a_8 = (-4x^6) \times (5^7 \times x^{2\times7})$ $\newline$ $a_8 = (-4x^6) \times (78125 \times x^{14})$
Multiply Terms: Multiply the terms together: $\newline$ $a_8 = -4 \times 78125 \times x^{(6+14)}$ $\newline$ $a_8 = -312500 \times x^{20}$