In a certain sequence of numbers, a1, a2, a3, ..., an, the average (arithmetic mean) of the first m consecutive terms starting with a1 is m, for any positive integer m. If a1=1, what is a13?
Choices.
A) 100  B) 55  C) 25  D) 19  E) 1
As stated above, (a1+a2+a3......+a13)/13=13   therefore a1+a2+a3.......a13=169 (1)   using the same logic, we got a1+a2+a3..........+a12=144 (2)   (2)-(1) we got a13=25   25
<result>C</result>
In a certain sequence of numbers, a1, a2, a3, ..., an, the average (arithmetic mean) of the first m consecutive terms starting with a1 is m, for any positive integer m. If a1=1, what is a13?