Math Is Fun Forum

Natasha99

Member

Registered: 2008-02-21

Posts: 1

Have you ever heard about the Penny Problem (grade 10 question) ?

I have got an assigment, and I can't find the nth term.

Natasha99

Member

Registered: 2008-02-21

Posts: 1

Re: Have you ever heard about the Penny Problem (grade 10 question) ?

Please reply if you'd like to help me out

Natasha99

Member

Registered: 2008-02-21

Posts: 1

Re: Have you ever heard about the Penny Problem (grade 10 question) ?

n  tn
1  1
2  7
3  19
4  37
5  61
6  91

So I've figured out that the difference between two terms increases by 6, but can't figure out how to represent this so that I can figure out an nth term (say 10, 100, or 100).

Ricky

Moderator

Registered: 2005-12-04

Posts: 3,791

Re: Have you ever heard about the Penny Problem (grade 10 question) ?

There is a method called guess and subtract.  I'm going to guess that your sequence has an "x^2" in it.  So what I do is subtract out x^2 from each number:

n  tn
1  1
2  7
3  19
4  37
5  61
6  91

n
1 0
2 3 = 1 * 3
3 10 ~ 3 * 3
4 21 = 3 * 7
5 36 = 3 * 9

I now notice some patter with 3, so instead of subtracting out x^2, I'll subtract out 3x^2

n 
1  -2
2  -5
3  -8
4  -11
5  -14
6  -17

Now it should become obvious.  That remaining sequence is f(n) = -3n + 1.  Therefore, our final answer is 3n^2 - 3n + 1

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