Answer
$d=3$
$a_5=-t+12$
The $n^{th}$ term is given by: $a_n = -t+3(n-1)$
$a_{100} = -t+297$
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,
$d=(-t+3)-(-t)
\\d=-t+3+t
\\d=(-t+t)+3
\\d=3$
The fifth term $a_5$ can be found by adding the common difference $3$ to the fourth term.
The fourth term of the sequence is $-t+9$.
Thus,
$a_5 = -t+9+3
\\a_5=-t+12$
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 $a=-t$ and $d=3$.
Thus, the $n^{th}$ term is given by:
$a_n = -t+3(n-1)$
Substituting 100 to $n$ gives the 100th term as:
$a_{100} = -t+3(100-1)
\\a_{100} = -t+3(99)
\\a_{100} = -t+297$
