Math Is Fun Forum

EbenezerSon

Member

Registered: 2013-07-04

Posts: 554

Geometric Progression problem

Hi Tutor;

On commencing employment a man is paid a salary of $720,000 per annum and receives annual increments of $35000, determine his salary in the 9th year and calculate the total salary he will receive in the first 12 yrs.
I had $1000000 as answer. But I'm getting hard time getting the   common ratio so that it will help me use the  GEOMETRIC PROGRESSION method to calculate for the first 12yrs.
Please help.

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I know only one thing - that is that I know nothing

Bob

Administrator

Registered: 2010-06-20

Posts: 10,619

Re: Geometric Progression problem

hi EbenezerSon

That's because it is not a geometric progression.  To be a GP there would have to be a common ratio between successive terms; 1st/2nd = 2nd/3rd = 3rd/4th and so on.

But the amount of the increase is a fixed sum irrespective of the salary that year.  What you have here is an arithmetic progression; first term = 720 000 and with a common difference of 35 000.  Do you know the formulas for an AP ?

I know only one thing - that is that I know nothing

But that means that if you know nothing you don't even know one thing !  You have created an interesting paradox.  And I suspect you know it.  So now you know two things. 

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

EbenezerSon

Member

Registered: 2013-07-04

Posts: 554

Re: Geometric Progression problem

Thank you Bob!
"I know only ...I know nothing"  I have always loved this paradox. Thanks for the compliment. I used AP to calculate for the 9th year and had the answer. Should I use AP To find for the 12th year?
Many thanks!

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I know only one thing - that is that I know nothing

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Geometric Progression problem

Hi;

If you are adding 35000 each time then that is an AP, so go ahead.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

Bob

Administrator

Registered: 2010-06-20

Posts: 10,619

Re: Geometric Progression problem

The total for 12 years is the 'sum of an AP'

Bob

---

Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

EbenezerSon

Member

Registered: 2013-07-04

Posts: 554

Re: Geometric Progression problem

So, regarding the formula above, is the [n] going to be 12? In other words,  is n = 12?
Please,  work the problem so that I follow your steps.
Thanks

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I know only one thing - that is that I know nothing

bobbym

bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

Re: Geometric Progression problem

Hi;

Let us see what is going on.

You can see that by the end of the 9th year he is making 1,000,000 dollars.

The formula to get that 9th term is:

where a is the starting amount (720,000), n is the term you want (9th in this case) and d is the common difference

To get how much he earned in 12 years:

How about checking this manually:

Also, remember these are arithmetic progressions not geometric.

---

In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
Always satisfy the Prime Directive of getting the right answer above all else.

EbenezerSon

Member

Registered: 2013-07-04

Posts: 554

Re: Geometric Progression problem

I see now!
Thank you

In an arithmetic progression, the 8th term is twice the 4th and the 20th is 40.
Find the first term. the common difference and the sum of the terms from the 8th term to the 20th term inclusive.

I'm gettin hard time solving it, please let me see yous steps.

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I know only one thing - that is that I know nothing

Bob

Administrator

Registered: 2010-06-20

Posts: 10,619

Re: Geometric Progression problem

hi EbenezerSon

In an arithmetic progression, the 8th term is twice the 4th and the 20th is 40.
Find the first term. the common difference and the sum of the terms from the 8th term to the 20th term inclusive.

I would start by calling the first term 'a', and the common difference 'd'.  Then write the information as equations:

4th term is a + 3d;  8th term is a + 7d;  20th is a + 19d

=> a + 7d = 2(a + 3d)

and a + 19d = 40

Solve these and the problem is nearly done.

Bob

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Children are not defined by school ...........The Fonz
You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei
Sometimes I deliberately make mistakes, just to test you!  …………….Bob

EbenezerSon

Member

Registered: 2013-07-04

Posts: 554

Re: Geometric Progression problem

Thank you Bob!

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I know only one thing - that is that I know nothing

EbenezerSon

Member

Registered: 2013-07-04

Posts: 554

Re: Geometric Progression problem

I had a = 2 and d = 2.
So after these should I proceed to use the AP sum formula to calculate seperately for the 8th and the 20th term?

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I know only one thing - that is that I know nothing

EbenezerSon

Member

Registered: 2013-07-04

Posts: 554

Re: Geometric Progression problem

Good one

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I know only one thing - that is that I know nothing