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- Aug 10th 2008, 07:02 PM #1

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## Help please!!!

It is only the 3rd day of my geometry class and I am already lost. I can tell this will be a good year!I just barely got a C in Algebra last year and now geometry is CRAZY!! I get so aggravated and I almost cry.I was always good in school...until High School. Anyway......I need help with this problem soon!!

Describe a pattern in the sequence of numbers. Predict the next number.

8, 15, 29, 57

I got that when you subtract 29 from 57 you get 28. 29-15=14 and 15-8=7

So that is x by 2 but how do I get that wrote down??

This is what I feel like doing right now.

- Aug 10th 2008, 08:37 PM #2

- Aug 11th 2008, 03:27 AM #3

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This looks like an arithmetic progression whose difference between members seems to grow.

What does this have to do with geometry?

Anyway, if you are not sure how to describe the solution, listen to your mind and exactly what words occur when you are thinking about the solution. I have observed that it is not always possible, or at least not always good enough, to describe the solution of a maths problem using only mathematical signs. I am not familiar with the US education system, but I believe you should be permitted to use English words to present your solution.

- Aug 11th 2008, 07:36 AM #4

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Indeed! Predicting the terms of an arithmetic sequence is a form of inductive reasoning.

**<From SparkNotes>**Two of the most basic methods of mathematical reasoning are inductive and deductive reasoning. They are both useful ways to arrive at conclusions, and are both very important to the study of geometry. Deductive reasoning is used more heavily than inductive reasoning in geometry, but in all of mathematics, including some of geometry, the process of deductive reasoning is only possible after inductive reasoning has led a mathematician to hypothesize about a given situation: only after a proof has been attempted can a mathematician's hypothesis be verified or refuted.**<SparkNotes>**

For instance, determine the sum of the interior angles of an n-gon.

Setup a table starting with the simplest polygon, a triangle. Use inductive reasoning to arrive at the formula. Note: the diagonals are drawn from one vertex, only.

3 sides 0 diagonals 1 triangle 180 degrees (180)(1)

4 sides 1 diagonal 2 triangles 360 degrees (180)(2)

5 sides 2 diagonals 3 triangles 540 degrees (180)(3)

6 sides 3 diagonals 4 triangles 720 degrees (180)(4)

7 sides 4 diagonals 5 triangles 900 degrees (180)(5)

.

.

.

**n sides**__(n-3) diagonals____(n-2) triangles__**180(n-2) degrees**

Studying the pattern, you can easily see that the number of triangles formed is always 2 less than the number of sides.

- Aug 11th 2008, 10:18 AM #5

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- Aug 11th 2008, 11:17 AM #6

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Relevant, yes. It's the idea of thinking inductively or deductively that has to do with geometry or any other math. True, the problem as stated by the OP is abstract, but math is all about establishing foundations and building on them. This would be a nice topic to discuss in the forum's Philosophy of Mathematics area. Start a thread and see what others think.

- Aug 13th 2008, 12:05 PM #7
For all but the first I can give you a formula how to calculate the elements of this sequence:

According to your considerations you have:

where n is the number of the element in the sequence.

So you have a geometrical sequence whose values are translated up by 8 units.