GRE Cumulative addition problem.

Question

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?

Answer 1

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

Now 160 + 161 + 322 + 644 + 1288 = ...

Answer 2

The question is how much did Molly earn in total, not in the last two-week period. The mysterious 'additional $\$1287$' is simply the sum of all earlier earnings: $$1287 = 160+161+322+644$$ hence her total earning is $$160+161+322+644 + 1288 = 2575$$

Answer 3

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 $=160+161+322++644+1288=2575$