Question 29
Suppose that $\{a_{n}\}_{n \geq 1}$ is an arithmetic sequence of real numbers such that
$$
\begin{array}{r}
a_{1}+a_{2}+a_{3}+a_{4}+\cdots+a_{10}=20 \\
a_{1}+a_{4}+a_{9}+a_{16}+\cdots+a_{100}=18
\end{array}
$$
Compute $a_{1}+a_{8}+a_{27}+a_{64}+\cdots+a_{1000}$.
$$
\begin{array}{r}
a_{1}+a_{2}+a_{3}+a_{4}+\cdots+a_{10}=20 \\
a_{1}+a_{4}+a_{9}+a_{16}+\cdots+a_{100}=18
\end{array}
$$
Compute $a_{1}+a_{8}+a_{27}+a_{64}+\cdots+a_{1000}$.