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

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Answer

So, the 7th term of the geometric sequence is $- 12288 x^{18}$ .

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 $- \frac{12 x^{8}}{- 3 x^{6}} = - 4 x^{2}$ .

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 $- 3 x^{6} \times (- 4 x^{2})^{6}$ .

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

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

Find the 7 th term of the geometric sequence shown below.−3x6,12x8,−48x10,…

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