#### Answer

$d=1.5$
$a_5=31$
The $n^{th}$ term is given by: $a_n = 25+1.5(n-1)$
$a_{100} = 173.5$

#### Work Step by Step

The sequence is arithmetic so the terms have a common difference.
The common difference $d$ can be found by subtracting any term to the next term in the sequence.
Thus,
$d=26.5-25
\\d=1.5$
The fifth term $a_5$ can be found by adding the common difference $1.5$ to the fourth term.
The fourth term of the sequence is $29.5$.
Thus,
$a_5 = 29.5+1.5
\\a_5=31$
The $n^{th}$ term $a_n$ of an arithmetic sequence is given by the formula $a_n = a+d(n-1)$ where $a$ = first term and $d$ = common difference.
The sequence has $a=25$ and $d=1.5$.
Thus, the $n^{th}$ term is given by:
$a_n = 25+1.5(n-1)$
Substituting 100 to $n$ gives the 100th term as:
$a_{100} = 25+1.5(100-1)
\\a_{100} = 25+1.5(99)
\\a_{100} = 25+148.5
\\a_{100} = 173.5$