Question 150
A sequence of 2019 numbers $a_{1}, a_{2}, a_{3}, \ldots, a_{2019}$ is given. It is known that, choosing any 4 consecutive terms of the sequence, their sum is constant. Similarly, taking two consecutive numbers, their difference in absolute value is constant (that is, $\left|a_{1}-a_{2}\right|=\left|a_{2}-a_{3}\right|=\left|a_{3}-a_{4}\right|=\ldots$ ).
It is also known that $a_{1} \lt a_{2} \lt a_{3}$ and that $a_{2}=6$. What is the sum of all the numbers of the sequence?
(A) 2019
(B) 2020
(C) 4038
(D) 12114
(E) The data are not sufficient to determine it
It is also known that $a_{1} \lt a_{2} \lt a_{3}$ and that $a_{2}=6$. What is the sum of all the numbers of the sequence?
(A) 2019
(B) 2020
(C) 4038
(D) 12114
(E) The data are not sufficient to determine it