Question

512,256,128,64 what is the conjecture

Answer 1

We are given sequance 512,256,128,64.

We can clealry see that each current term is being divided by 2 to get next term.

In order ways we could say that if we divide next term from previous term, we get 1/2.

We can see, all ratios are same.

So, this is a geomatric sequance.

We know the formula for geomatric sequence

$a_n = ar^{n-1}$

Where a is the first term of the sequance, r is the common ratio and n is the number of terms.

We got first term a=512, and coomon ratio r= 1/2.

Plugging those values of a and r in formula, we get

$a_n =512(\frac{1}{2})^{n-1$