Tough Sequence Question..or maybe not?

Question

1, _, _, 1/64

Fill in the blanks in this sequence with as many solutions as you can.

So far I got: 1/4, 1/16 or 4 and 16

I think there are MANY solutions not just 3, its an extra credit problem

Answer 1

1 (= 64/64), then 43/64, 22/64, and 1/64 - decreasing by 21/64 each time.

Or 1 (= 64/64), then 57/64, 36/64, 1/64 - decreasing by 7/64, 21/64 and 35/64 which increase by 14/64 each time.

I think the teacher will get suspicious if you turn in anything more complicated than your own solution and these two.

Answer 2

The series appears to be 1/(4^(n-1)), for n = 1, 2, 3,...

1/4⁰, 1/4¹, 1/4², 1/4³

So all you have to do is calculate 1/4¹ and 1/4², then simplify.

Answer 3

Tell you teacher that there are infinitely many sequences.
This "function" has the "points"
(1,1) and (4,1/64)
you can connect those points with a line, infinitely many parabolas, infinitely many cubic functions, sine functions, geometric sequences (as in, divide by 4 each time).... make some up! There are infinitely many numbers for the 2nd and third space.
If you're interested in finding some actual such equations (or rules) then you can email me at [e-mail]

Answer 4

Its 1/4 and 1/16

You just divide by 4 every time

Answer 5

1/16, 1/32

Answer 6

1, .... , .... , 1/64, ....
= 4^0, 4^(--1), 4^(--2), 4^(--3), 4^(--5), ....