Respuesta :
We see that there is a difference of 4 between each number:
[tex]\begin{gathered} -23-4=-27 \\ -27-4=-31 \\ -31-4=-35 \end{gathered}[/tex]and so on. Then, we can propose the following formula:
[tex]a_n=-23-4\cdot n[/tex]For instance, when n=0 we have
[tex]\begin{gathered} a_0=-23+0 \\ a_0=-23 \end{gathered}[/tex]when n=1, we have
[tex]\begin{gathered} a_1=-23-4\cdot1 \\ a_1=-23-4 \\ a_1=-27 \end{gathered}[/tex]when n=2, we have
[tex]\begin{gathered} a_2=-23-4\cdot2 \\ a_2=-23-8 \\ a_2=-31 \end{gathered}[/tex]and so on. Then, in order to compute the 78th term, we must substitute n=78 in our formula. It yields,
[tex]\begin{gathered} a_{78}=-23-4\cdot78 \\ a_{78}=-23-312 \\ a_{78}=-335 \end{gathered}[/tex]and the answer is -335
