Question 29
It is known that each term of sequence $\{a_n\}$ is a non-zero real number, and for any positive integer $n$ holds the equation
$$
(a_1 + a_2 + \cdots + a_n)^2 = a_1^3 + a_2^3 + \cdots + a_n^3.
$$
(1) When $n = 3$, find out all the sequences consisting of three terms $a_1, a_2, a_3$.
(2) Does there exist an infinite sequence $\{a_n\}$ such that $a_{2013} = -2012$? If it exists, write out the formula of general term; if not, give your reason.
$$
(a_1 + a_2 + \cdots + a_n)^2 = a_1^3 + a_2^3 + \cdots + a_n^3.
$$
(1) When $n = 3$, find out all the sequences consisting of three terms $a_1, a_2, a_3$.
(2) Does there exist an infinite sequence $\{a_n\}$ such that $a_{2013} = -2012$? If it exists, write out the formula of general term; if not, give your reason.