Question

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

Answer 1

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.