5 ,1 ,-3,-7 ? what the dickens is going on?
notice, from 5 to 1, is really -4 units,
from 1 to -3, is -4 units as well, 1 -4 = -3 and so on.
so, to get the next term's value, you simply subtract 4 from the current one, namely -4 is the "common difference".
and we also know the first term is 5, ok... then
[tex]\bf n^{th}\textit{ term of an arithmetic sequence}\\\\
a_n=a_1+(n-1)d\qquad
\begin{cases}
n=n^{th}\ term\\
a_1=\textit{first term's value}\\
d=\textit{common difference}\\
----------\\
d=-4\\
a_1=5\\
n=100
\end{cases}
\\\\\\
a_{100}=5+(100-1)(-4)\implies a_{100}=5+(99)(-4)
\\\\\\
a_{100}=5-396\implies a_{100}=-391[/tex]
