Answer
$d=-2.7$
$a_5=4.2$
The $n^{th}$ term is given by: $a_n=15-2.7(n-1)$
$a_{100} = -252.3$
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,
$d=12.3-15
\\d=-2.7$
The fifth term $a_5$ can be found by adding the common difference $-2.7$ to the fourth term.
The fourth term of the sequence is $6.9$.
Thus,
$a_5 = 6.9+(-2.7)
\\a_5=4.2$
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 $a=15$ and $d=-2.7$.
Thus, the $n^{th}$ term is given by:
$a_n = 15+(-2.7)(n-1)
\\a_n=15-2.7(n-1)$
Substituting 100 to $n$ gives the 100th term as:
$a_{100} = 15-2.7(100-1)
\\a_{100} = 15-2.7(99)
\\a_{100} = 15-267.3
\\a_{100} = -252.3$
