Answer
$d=s$
$a_5=2+4s$
The $n^{th}$ term is given by: $a_n = 2+s(n-1)$
$a_{100} = 2+99s$
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,
$d=(2+s)-2
\\d=2+s-2
\\d=s$
The fifth term $a_5$ can be found by adding the common difference $s$ to the fourth term.
The fourth term of the sequence is $2+3s$.
Thus,
$a_5 = 2+3s+s
\\a_5=2+4s$
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 $a=2$ and $d=s$.
Thus, the $n^{th}$ term is given by:
$a_n = 2+s(n-1)$
Substituting 100 to $n$ gives the 100th term as:
$a_{100} = 2+s(100-1)
\\a_{100} = 2+s(99)
\\a_{100} = 2+99s$
