Both the ai and the bi are symmetrical about zero, so their sum will be zero. Any multiple of their sum will also be zero, and any combination involving their sum or multiples thereof will be zero.
63. The sum is zero.
[tex] \bf \begin{array}{cccll}
&a\\
x&&y\\
\text{\textemdash\textemdash\textemdash}&&\text{\textemdash\textemdash\textemdash}\\
1&&-4\\
2&&-2\\
3&&0\\\
4&&2\\
5&&4
\end{array}\qquad \qquad
\begin{array}{cccll}
&b\\
x&&y\\
\text{\textemdash\textemdash\textemdash}&&\text{\textemdash\textemdash\textemdash}\\
1&&4\\
2&&2\\
3&&0\\
4&&-2\\
5&&-4
\end{array}\\\\
------------------------------- [/tex]
[tex] \bf \sum\limits_{i=1}^{5}~(2a_i+b_i)
\\\\\\
\stackrel{i=1}{2a_1+b_1}\implies 2(-4)+(4)\implies -4
\\\\\\
\stackrel{i=2}{2a_2+b_2}\implies 2(-2)+(2)\implies -2
\\\\\\
\stackrel{i=3}{2a_3+b_3}\implies 2(0)+(0)\implies 0
\\\\\\
\stackrel{i=4}{2a_4+b_4}\implies 2(2)+(-2)\implies 2
\\\\\\
\stackrel{i=5}{2a_5+b_5}\implies 2(4)+(-4)\implies 4\\\\
-------------------------------\\\\
(-4)+(-2)+(0)+(2)+(4)\implies \boxed{0} [/tex]
