# 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?

Feb 23, 2017

${a}_{n} = 64 \setminus \times {\left(\setminus \frac{1}{2}\right)}^{n - 1}$

#### Explanation:

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

${a}_{k} = \setminus \frac{1}{2} {a}_{k - 1}$

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

${a}_{n} = 64 \setminus \times {\left(\setminus \frac{1}{2}\right)}^{n - 1}$