How do you write a rule for the nth term of the geometric sequence given the two terms $a_3=5, a_6=5000$ ?

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Answer 1 · 2017-03-19T07:16:06

Rule for the $n^(th)$ term of the geometric sequence is $a_n=10^(n-1)/20$

If $m^(th)$ term of a geometric sequence is $a_m$ and $n^(th)$ term of the sequence is $a_n$ , then the common ratio $r$ is given by

$r=(a_n/a_m)^(1/((n-m)))$

Here, we have $a_3=5$ and $a_6=5000$ , hence

$r=(5000/5)^(1/((6-3)))=1000^(1/(3))=root(3)1000=10$

and as $n^(th)$ term of a geometric sequence is given by

$a_n=a_1xxr^(n-1)$ and hence as $a_3=5$

$a_1=a_n/r^(n-1)=5/10^2=0.05$

and rule for the $n^(th)$ term of the geometric sequence is

$a_n=0.05xx10^(n-1)=10^(n-1)/20$

How do you write a rule for the nth term of the geometric sequence given the two terms a_3=5, a_6=5000a_3=5, a_6=5000?