[ Recurrence relations ]  $[\quad \underline{\text { C }}$ mean values $]$

Thirteen turkey chicks pecked at grains. The first turkey chick pecked 40 grains; the second - 60, each subsequent chick pecked the average number of grains pecked by all previous chicks. How many grains did the 10th turkey chick peck?
Recall the properties of the arithmetic mean.

## Solution

The third turkey chick pecked $(40+60): 2=50$ points. Each subsequent one also pecked 50 grains: if you add a number equal to the arithmetic mean of a group of numbers to that group, the arithmetic mean of the new group will be equal to the arithmetic mean of the initial group.

## Answer

50 grains.