For Discrete Mafhmatics

$1)$ The $4$ th term of an arithmetic sequence is $6$ and the $15$ th term is $14.$ What is the $100$ th term?

$2)$ What is the general formula for the geometric sequence $8,-6,4\mathrm{.}5,-3\mathrm{.}375,$dots

$3)$ Write the repeating decimal $0\mathrm{.}5555555$dots as a fraction using the geometric series.