Question

Elaborate something for me:

Identify a pattern and find the next number in the pattern.

–0.8, –3.2, –12.8, –51.2
I know the next number is -204.8, I got this by dividing -3.2 by -0.8. I was wondering how I could write this into an equation?
\((n) \times 4\)?

Answer 1

1) You do now know THE next number is -204.8. You know only that IF the pattern is (n)*4, THEN the next number in the sequence is -204.8.

2) You have noticed A pattern. There are infinitely many more patterns. I am delighted that this question is worded very well. It says to find A pattern and subsequently produce the next value, based on this pattern.

3) Try \(f(n) = -0.8 * 4^{n-1}\) for n in 1, 2, 3, 4, ... (The Natural Numbers)

Answer 2

** Typo Alert **

The above should say "You do not know...", rather than "You do now know..."

** End of Alert **

Answer 3

Nice work, tkhunny! Your 3) is the way to go. And thanks for your Typo Alert!

Another way to begin builds upon your observation that -0.8 is a common factor of the given sequence. Factoring out -0.8 results in the following: -0.8*{1, 4, 16, 64}.

This makes it just a little easier to recognize that we have the sequence 4^(n-1) inside the brackets.

Answer 4

Keep in mind my number 2). There ARE infinitely many patterns matching these four numbers. ANY pattern you can justify and prove should be an acceptable response to this question. Personally, I would pick a much stranger pattern than simply multiplying by 4. This would possibly generate some useful, learning conversation between me and my mentor.

Answer 5

Actually, tkhunny, we're multiplying powers of 4 by -0.8: -0.8*4^n, with n: {0, 1, 2, 3, ... }.

Answer 6

There are many ways to describe the same pattern. You can index any way you like. There is NOT just one way to think about it. This is the lesson we should learn.