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3,-12,48,-192 7th term

1 Answer

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In this question we have numbers that create a geometric sequence, where each number is the previous one multiplied by a common ratio.

In order to find this ratio, we just need to divide one term by the previous term:


\text{ratio}=-(12)/(3)=-4

Now, to find the 7th term, we can use the formula:


a_n=a_1\cdot q^(n-1)

Where a1 is the first term and q is the common ratio. Using n = 7, we have:


\begin{gathered} a_7=3\cdot(-4)^6 \\ a_7=3\cdot4096 \\ a_7=12288 \end{gathered}

So the 7th term of this sequence is 12,288.

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