Grade 8

[Racheloakes]

I am looking to figure out an equation for this question! I know the answers, but I am stuck on an equation!
If you collect 1 rock on Monday and you collect twice as many each day as the day before, how many rocks will you have in a week, two weeks, a month- no month specified in my question but let’s say April.

 

[Racheloakes]

I know that m=1 tues=2. We’d =4. Thurs=8 frid=16 and so forth but
When you get into bigger number such as the 30th day in a month which 536,870,912!
I am trying to figure out an algorithm or equation as I could not do this for 4 months

 

[lev888]

I know that m=1 tues=2. We’d =4. Thurs=8 frid=16 and so forth but
When you get into bigger number such as the 30th day in a month which 536,870,912!
I am trying to figure out an algorithm or equation as I could not do this for 4 months

What topic are you studying?

 

[Deleted member 4993]

I am looking to figure out an equation for this question! I know the answers, but I am stuck on an equation!
If you collect 1 rock on Monday and you collect twice as many each day as the day before, how many rocks will you have in a week, two weeks, a month- no month specified in my question but let’s say April.

Have studied Geometric sequence and sum of geometric series?

 

[pka]

I know that m=1 tues=2. We’d =4. Thurs=8 frid=16 and so forth but
When you get into bigger number such as the 30th day in a month which 536,870,912!
I am trying to figure out an algorithm or equation as I could not do this for 4 months

You have some mistaken views on how this works.
On the first day, Sunday, you collect one stone. That is \(2^0\)
On Monday you collect two more stones. That is \(2^1=2\), for a total of three.
On Tuesday you collect four more stones. That is \(2^2=4\), for a total of seven.
By Saturday, the seventh day, you collect \(2^6\) more stones, for a total of \(1+2+4+\cdots+2^6=127\). SEE HERE
On the thirtieth day you collect \(2^{29}\) more stones for a total of \(\sum\limits_{k = 0}^{29} {{2^k}}=1073741823 \) SEE HERE
Use that website to see that is \(2^{30}-1\)