How do you write a rule for the nth term of the geometric sequence given the two terms $a_2=4, a_5=256/27$ ?

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Answer 1 · 2018-06-26T09:48:49

$a_n = 3*(4/3)^(n-1)$

The geometric $n^"th"$ term is $a_n = ar^(n-1)$

Where $a$ is the first term

$ar = 4$

$ar^4 = 256/27$

$=> a = 4/r$

$=> 4/r * r^4 = 256/27$

$=> 4r^3 = 256/27$

$=> r = 4/3$

$=> a = 4/r = 4/(4/3) = 3$

$=> a_n = 3*(4/3)^(n-1)$

How do you write a rule for the nth term of the geometric sequence given the two terms a_2=4, a_5=256/27a_2=4, a_5=256/27?