GRE Cumulative addition problem. The following problem is quoted from Manhattan 5lb Book of GRE Practice Problems, 2016ed.

Question: Molly worked at an amusement park over the summer. Every two weeks she was paid according to the following schedule: at the end of 1st $2$ weeks, she received \$$160$. At the end of each subsequent 2-week period, she received \$$1$, plus an additional amount equal to the sum of all payments she had received in the previous weeks. How much money was Molly paid during the full $10$ weeks of summer?
Solution: \$$2575$

I am not sure why Molly received \$ $2575$ at the end of 10 week. To my understanding, she should receive \$ $1288$.
My understanding is the following
Weeks        Paid
  2          160
  4          1+160 = 161
  6          1+161+160 = 322
  8          1+322+161+160 = 644
  10         1+644+322+161+160 = 1288   

Why was additional \$$1287$ paid?
Can anyone explain?

I will give a brief explanation
In $2$ weeks she earned $=160$
In the next two weeks she earned $=1+160=161$
In the next two weeks she earned $=1+161+160=322$
In the next two weeks she earned $=1+161+160+322=644$
In the final two weeks she earned $=1+322+161+160+644=1288=>$ Note that $1288$ is the amount she earned in last $2$ weeks
Now we need to add the total amount $=160+161+322++644+1288=2575$
