Respuesta :
The sequence can be found using an arithmetic sequence:
[tex]a_n=a_1+(n-1)d[/tex]Where:
a1 = First term
d = Common difference
so:
[tex]\begin{gathered} a_2=-8.5=-12+(2-1)d \\ -8.5=-12+d \\ d=12-8.5 \\ d=3.5 \end{gathered}[/tex]Therefore, the sequence is given by:
[tex]\begin{gathered} a_n=-12+(n-1)\cdot3.5 \\ a_n=3.5n-15.5 \end{gathered}[/tex]Let's find the limit of the function associated to an:
[tex]\begin{gathered} \lim _{n\to\infty}a_n=\lim _{x\to\infty}f(x) \\ where \\ f(x)=3.5x-15.5 \\ so\colon \\ \lim _{x\to\infty}(3.5x-15.5)=\lim _{x\to\infty}3.5x=3.5\lim _{x\to\infty}x=3.5\cdot\infty=\infty \end{gathered}[/tex]Therefore, since the limit of the function associated to the sequence tends to infinity, we can conclude that the sequence diverges
