# 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

mafalexpicsak 2022-10-16 Answered
Write the first five terms of the geometric sequence ${a}_{1}=64,{a}_{k+1}=\frac{1}{2}{a}_{k}$ and determine the common ratio and write the nth term of the sequence as a function of n
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## Answers (1)

Zackary Mack
Answered 2022-10-17 Author has 12 answers
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
${a}_{n}=64×{\left(\frac{1}{2}\right)}^{n-1}$
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