Finding the terms (a) of the serie:
[tex]\begin{gathered} a1=-40 \\ a2=-25 \\ a3=-10 \\ a4=5 \end{gathered}[/tex]In the aritmetic serie, we have a constant which is always added to the term, in order to find the next.
If you observe:
a2-a1 = -25 -(-40) = -25+40 = 15
a3-a2 = -10 - (-25) = -10 +25 = 15
So, in this serie, the constant is 15. That means, to find the next term, we have to add 15 units to the actual term:
[tex]\begin{gathered} a4\text{ = a3 + 15 = -10+15 = +5} \\ a5\text{ = a4 + 15 = 5 +15 = 20} \\ a6\text{ = a5 + 15 = 20 +15 = 35} \\ a7\text{ = a6+15 = 35 +15 = 50} \end{gathered}[/tex]Now we have the 7 terms:
-40 -25 -10 +5 +20 +35 + 50
And the sum is: -40 + (-25) + (-10) + 5 + 20 + 35 + 50
= 35
