1. ## arithmetic sequence problem

Hello

Here's the question I need a hand with:

You have a 10-year plan to raise money for university. You have the choice of two jobs:

The first has a commencing salary of $30 000 per year with an annual increment of$1000

The second offers a commencing salary of $31 000 per year with a six monthly increment of$500

Over 10 years which job would pay the most and by how much?

Thanks in advance, all help is much appreciated.

2. Originally Posted by listeningintently
Hello

Here's the question I need a hand with:

You have a 10-year plan to raise money for university. You have the choice of two jobs:

The first has a commencing salary of $30 000 per year with an annual increment of$1000

The second offers a commencing salary of $31 000 per year with a six monthly increment of$500

Over 10 years which job would pay the most and by how much?

Thanks in advance, all help is much appreciated.
YOu say this is an arithmetic sequence. Don't you know any formulas for summing arithmetic sequences?

3. haha...funny...

Yes, I am aware of these formulas, I simply wanted a hand with how to figure out the second case as the answers in my book differed to the one I received.

4. Originally Posted by listeningintently
The first has a commencing salary of $30 000 per year with an annual increment of$1000
At the 0-th zero you have $\displaystyle 30000+(0)(1000)$
At the 1-st zero you have $\displaystyle 30000+(1)(1000)$
At the 2-nd zero you have $\displaystyle 30000+(2)(1000)$
...
In general at the 10th year you have $\displaystyle 30000+(10)(1000)$

The second offers a commencing salary of $31 000 per year with a six monthly increment of$500
Similar reasoning says that at the 10-th you have $\displaystyle 31000 + (10)(500)$

Now which one is bigger?