Because at the end of each week he sells k chickens, there are weeks of selling (and rearing).
1st week : 1000x0.5
2nd week : (1000-k)x0.5
3rd week : (1000-2k)x0.5
th week : because so far, he has sold chickens.
th week :
So the total is :
Oh yeah, this is awful...
Factoring by 0.5, we get :
You can see that 1000 minus the red terms belong to an arithmetic sequence of general term : , starting at n=0, finishing at n= , and of progression -k
---> there are terms.
This is the formula you should know. But we're starting at a_0, so it's different
If something is unclear, tell me.. And if you think there is an easier way.. I'd agree with you