Answer
$d=-18$
$a_5=-43$
The $n^{th}$ term is given by: $a_n=29-18(n-1)$
$a_{100} = -1753$
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,
$d=11-29
\\d=-18$
The fifth term $a_5$ can be found by adding the common difference $-18$ to the fourth term.
The fourth term of the sequence is $-25$.
Thus,
$a_5 = -25+(-18)
\\a_5=-43$
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 $a=29$ and $d=-18$.
Thus, the $n^{th}$ term is given by:
$a_n = 29+(-18)(n-1)
\\a_n=29-18(n-1)$
Substituting 100 to $n$ gives the 100th term as:
$a_{100} = 29-18(100-1)
\\a_{100} = 29-18(99)
\\a_{100} = 29-1782
\\a_{100} = -1753$