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 a15?
Choose the correct choice from the following answers.
A) 100 B) 55 C) 29 D) 19 E) 1
As stated above, (a1+a2+a3......+a15)/15=15   therefore a1+a2+a3.......a15=225 (1)   using the same logic, we got a1+a2+a3..........+a14=196 (2)   (2)-(1) we got a15=29   29
<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 a15?