How do you write the first five terms of the geometric sequence $a_1=81, a_(k+1)=1/3a_k$ and determine the common ratio and write the nth term of the sequence as a function of n?

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How do you write the first five terms of the geometric sequence $a_1=81, a_(k+1)=1/3a_k$ and determine the common ratio and write the nth term of the sequence as a function of n?

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Answer 1 · 2017-03-27T14:47:07

First five terms are ${81,27,9,3,1]$ , common ratio is $1/3$ and $n^(th)$ term $a_n=3^(5-n)$

Explanation:

In a geometric series common ratio $r$ is the ratio of term to its immediately preceding term. Here we have a term $a_k$ and as next term is $a_(k+1)$ and $a_(k+1)/a_k=1/3$ ,

we have $r=1/3$

AS given first term as $a_1$ and common ratio as $r$ , the $n^(th)$ term $a_n=a_1xxr^(n-1)$ . Now given first term $a_1=81$ and $r=1/3$

$n^(th)$ term $a_n$ is $81xx1/3^(n-1)$

= $3^4/3^(n-1)=3^(4-n+1)=3^(5-n)$

first five terms are ${81,81xx1/3=27,27xx1/3=9,9xx1/3=3,3xx1/3=1}$

i.e. ${81,27,9,3,1}$

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How do you write the first five terms of the geometric sequence $a_1=81, a_(k+1)=1/3a_k$ and determine the common ratio and write the nth term of the sequence as a function of n?

1 Answer

Explanation:

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Science

Math

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How do you write the first five terms of the geometric sequence a_1=81, a_(k+1)=1/3a_ka_1=81, a_(k+1)=1/3a_k and determine the common ratio and write the nth term of the sequence as a function of n?

1 Answer

Explanation:

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How do you write the first five terms of the geometric sequence $a_1=81, a_(k+1)=1/3a_k$ and determine the common ratio and write the nth term of the sequence as a function of n?