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:

$\text{ratio}=-\frac{12}{3}=-4$

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.