Question

Find the next three terms in this sequence: 5120, 1280, 320, 80...-160, -400, -64020, 5, 1.2540, 20, 1076, 72, 68

Answer 1

Given the first four terms of this sequence:

`(5120,1280,320,80,\ldots)`

We can see a pattern. To analize this pattern, let's first check the difference between those terms.

`\begin{gathered} 5120-1280=3840 \\ 1280-320=960 \\ 320-80=240 \end{gathered}`

From those differences, we can verify the following equations:

`\begin{gathered} 3840=4(960) \\ 960=4(240) \end{gathered}`

From this, we can write the general rule for this sequence:

`a_n=(5120)/(4^(n-1))`

This sequence gives us:

`\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}`

Then, we have the following 3 terms. (20, 5, 1.25)