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

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Answer 1 · 2017-02-23T10:00:23

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

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

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

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

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

How do you write the first five terms of the geometric sequence a_1=64, a_(k+1)=1/2a_ka1=64,ak+1=12aka_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?