Answer
$d=-3$
$a_5=-1$
The $n^{th}$ term is given by: $a_n=11-3(n-1)$
$a_{100} = -286$
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,
$d=8-11
\\d=-3$
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 $2$.
Thus,
$a_5 = 2+(-3)
\\a_5=-1$
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 $a=11$ and $d=-3$.
Thus, the $n^{th}$ term is given by:
$a_n = 11+(-3)(n-1)
\\a_n=11-3(n-1)$
Substituting 100 to $n$ gives the 100th term as:
$a_{100} = 11-3(100-1)
\\a_{100} = 11-3(99)
\\a_{100} = 11-297
\\a_{100} = -286$
