Question

wat is 24,12,6 to the 8th term. Round it to the nearest 1000

Answer 1

We can see that 24 divided by 2 is 12. Similarly, 12/2 is 6 and so on. Then, the sequence rule can be written as

$a_n=24(\frac{1}{2})^{n-1}_{}$

For instance,

$\begin{gathered} a_1=24(\frac{1}{2})^{1-1}=24(\frac{1}{2})^0=24\times1=24 \\ a_2=24(\frac{1}{2})^{2-1}=24(\frac{1}{2})=12 \\ a_3=24(\frac{1}{2})^{3-1}=24(\frac{1}{4})=6 \end{gathered}$

Then, by substituting n=8 (8th term) into the first equation, we have

$a_8=24(\frac{1}{2})^{8-1}=24(\frac{1}{2})^7=24\times\frac{1}{128}=0.1875$

therefore, by rounding to the nearest thousandth, the answer is 0.188.