Given the first four terms of this sequence:
[tex](5120,1280,320,80,\ldots)[/tex]We can see a pattern. To analize this pattern, let's first check the difference between those terms.
[tex]\begin{gathered} 5120-1280=3840 \\ 1280-320=960 \\ 320-80=240 \end{gathered}[/tex]From those differences, we can verify the following equations:
[tex]\begin{gathered} 3840=4(960) \\ 960=4(240) \end{gathered}[/tex]From this, we can write the general rule for this sequence:
[tex]a_n=\frac{5120}{4^{n-1}}[/tex]This sequence gives us:
[tex]\begin{gathered} a_1=5120 \\ a_2=1280 \\ a_3=320 \\ a_4=80 \\ a_5=20 \\ a_6=5 \\ a_7=1.25 \end{gathered}[/tex]Then, we have the following 3 terms. (20, 5, 1.25)
