Question

What is the 15th term of the sequence 400, 100, 25, 25/4...

Answer 1

This is a geometric series since it has a common ratio of 1/4

$T_n = 400( \dfrac{1}{4} )^{n-1}$

When n = 15
$T_{15} = 400( \dfrac{1}{4} )^{15-1}$

$T_{15} = 400( \dfrac{1}{4^{14}} )$

$T_{15} = \dfrac{400}{67108864} = \dfrac{25}{4194304}$