Question 130
A sequence $a_{1}, \ldots, a_{100}$ of real numbers is such that the arithmetic mean of two consecutive terms is always equal to the index of the second term (for example, $\frac{a_{4}+a_{5}}{2}=5$); what is the sum of the 100 numbers of the sequence?
(A) 2550
(B) 5050
(C) 5100
(D) 10100
(E) It cannot be determined: it depends on $a_{1}$.
(A) 2550
(B) 5050
(C) 5100
(D) 10100
(E) It cannot be determined: it depends on $a_{1}$.