Question

How do you write the first five terms of the geometric sequence `a_1=64, a_(k+1)=1/2a_k` and determine the common ratio and write the nth term of the sequence as a function of n?

Answer 1

`a_n = 64\times(\frac{1}{2})^(n-1)`

Explanation:

First, it's better to change the sequence and write that in this way:

`a_k = \frac{1}{2} a_(k-1)`

It's obvious that each term is half of the previous term, and by the definition of geometric sequence, we can write the equation very simple.

is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number, from wikipedia

`a_n = 64\times(\frac{1}{2})^(n-1)`