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?

1 Answer
Feb 23, 2017

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


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) #