Arithmetic Series

kerubiku

New member
Joined
Jul 4, 2020
Messages
1
Corey is deciding between two summer jobs. He plans to work from May to August, inclusive.

First job pays $1500/month with a monthly raise of $150

Second job pays $300/week with a weekly raise of $15

(a) Determine the total income earned if Corey takes the first job

(b) How many weeks are there during this time period

(c) Determine the total income earned if Corey takes the second job
 
Corey is deciding between two summer jobs. He plans to work from May to August, inclusive.

First job pays $1500/month with a monthly raise of $150

Second job pays $300/week with a weekly raise of $15

(a) Determine the total income earned if Corey takes the first job

(b) How many weeks are there during this time period

(c) Determine the total income earned if Corey takes the second job
The solution requires summation of geometric sequences (Geometric series). What have you learned about this series?

Please show us what you have tried and exactly where you are stuck.

Please follow the rules of posting in this forum, as enunciated at:

https://www.freemathhelp.com/forum/threads/read-before-posting.109846/#post-486520

Please share your work/thoughts about this assignment.
 
These are, as you say, arithmetic (not geometric) series. Have you learned any formulas related to that topic? Please tell us what you know, and show us what you have tried. Where do you need help?
 
I don't see any reason to use series, whether "arithmetic" or "geometric".
(a) First job pays $1500/month with a monthly raise of $150
Okay he earned $1500 in May, $1600+ 150= $1650 in June, $1650+ 150= $1800 in July, and $1800+ 150= $1950 in July.
How much do those add to?

"b) How many weeks are there during this time period?" and you didn't answer that so I suppose you want help with that?
"He plans to work from May to August, inclusive"
Okay that is "May, June, July, August". Now, how many weeks are there in each of those months?
(Go look on calendar If you have to! I might be inclined to include "half weeks" for each month.

(c) Determine the total income earned if Corey takes the second job
Okay, Since Corey is being paid per week, that number of week might just make it worth while to use the formula for an arithmetic series!
 
The monthly $150 is the same each month, not a percentage. The word raise is misleading. So four months just gives you 4 • 150 = 600 added to the total.
 
The monthly $150 is the same each month, not a percentage. The word raise is misleading. So four months just gives you 4 • 150 = 600 added to the total.
Did you compare your idea to post #4?

Each month, the monthly pay is increased, and the next month it is increased from that level, so each increase applies to more than one month. How is "raise" misleading?
 
Did you compare your idea to post #4?

Each month, the monthly pay is increased, and the next month it is increased from that level, so each increase applies to more than one month. How is "raise" misleading?

I didn't see that! Oh wow so it is! Student summer stipends, if varying by month, would normally just list the amounts as in #4 above. I guess "salary raise" made it sound like a permanent job.
 
No one said the situation was realistic. In doing math problems, you have to set aside some knowledge of the real world, and just use the information given.
 
No one said the situation was realistic. In doing math problems, you have to set aside some knowledge of the real world, and just use the information given.

Yes Dr Peterson. I am not good at this. When I try to help my kids with homework, they tell me, "That's not what the teacher wants."
 
Did you compare your idea to post #4?

Each month, the monthly pay is increased, and the next month it is increased from that level, so each increase applies to more than one month. How is "raise" misleading?
In Singleton's defense - raises are "generally" expressed as % of current pay. That's how I had "misinterpreted" the problem as GP.
 
Yes Dr Peterson. I am not good at this. When I try to help my kids with homework, they tell me, "That's not what the teacher wants."
In Singleton's defense - raises are "generally" expressed as % of current pay. That's how I had "misinterpreted" the problem as GP.
Which, of course, was my point in post #11: People who know math well in the real world may get it "wrong" in class, because class problems are typically different from the real world. (When real "real world" problems are given in class, they are much too complicated for beginners! And they fail to illustrate all the math we want to teach, because that would make them even worse.) On the other hand, I imagine math teachers often get it wrong in the real world, because they are not aware of how things really work.

Even ancient Egyptian math problems were highly artificial; this is part of the nature of teaching math.

On the other hand, reading the words of a problem carefully is important in both realms.
 
Top