How do you write an nth term rule for $5,-5/3,5/9,-5/27,...$ and find $a_6$ ?

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Answer 1 · 2018-04-28T23:06:52

See below

Geometric sequence explicit formula:
$a_n = a_1(r)^(n-1)$

Determine $r$ which is the decay factor:
$r=-5/3*1/5= -1/3$

Substitute into the equation for the rule:
$a_n = 5(-1/3)^(n-1)$

For the sixth term:
$a_6 = 5(-1/3)^(6-1)=-5/243$

How do you write an nth term rule for 5,-5/3,5/9,-5/27,...5,-5/3,5/9,-5/27,... and find a_6a_6?