Find the 7 th term of the geometric sequence shown below.
\[
-3 x^{6}, 12 x^{8},-48 x^{10}, \ldots
\]

Answer

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Answer

So, the 7th term of the geometric sequence is \(\boxed{-12288x^{18}}\).

Steps

Step 1 ：First, we need to find the common ratio of the geometric sequence. We can do this by dividing the second term by the first term, which gives us \(-\frac{12x^8}{-3x^6}= -4x^2\).

Step 2 ：Then, we can find the 7th term by multiplying the first term by the common ratio raised to the power of 6 (since the 7th term is 6 terms away from the first term). This gives us \(-3x^6 \times (-4x^2)^6\).

Step 3 ：Calculating the above expression, we get \(-3x^6 \times 4096x^{12} = -12288x^{18}\).

Step 4 ：So, the 7th term of the geometric sequence is \(\boxed{-12288x^{18}}\).

Find the 7 th term of the geometric sequence shown below.\[-3 x^{6}, 12 x^{8},-48 x^{10}, \ldots\]

Answer

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Find the 7 th term of the geometric sequence shown below.
\[
-3 x^{6}, 12 x^{8},-48 x^{10}, \ldots
\]