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### Course: Algebra (all content)>Unit 18

Lesson 9: Deductive and inductive reasoning

# Inductive reasoning

Sal analyzes a solution of a mathematical problem to determine whether it uses inductive reasoning. Created by Sal Khan and Monterey Institute for Technology and Education.

## Want to join the conversation?

• Is there a difference between a conjecture and an assumption?
• As I understand it, an assumption is to take something for granted, whereas a conjecture is an educated guess based on incomplete or inconclusive evidence.
• So is a conjecture in math kind of the same as a hypothesis in science?
• Yeah, kind of. The difference is that you verify a hypothesis with an experiment and you verify a conjecture with a proof, but they both involve finding the pattern in a pile of data and predicting something that you couldn't tell from that data directly.
• I look the series `0, 3, 8, 15, 24, 35...` and have a conjecture like this: First, +3 then +5 then +7 then +9 then +11. Obviously, the next number should be +13: `35 + 13 = 48`. Is my induction wrong? Or should I say there are more than a reasoning which you can apply to an arithmetic series?
• That seems like a reasonable conjecture based upon the pattern you've seen. Nice inductive reasoning! :) And you'll notice it agrees with the formula n^2 - 1 that Jill conjectured in Sal's video.

I'm not sure what you meant by your last question, though: "Or should I say there are more than a reasoning which you can apply to an arithmetic series?" I will note that this sequence, incidentally, is not arithmetic, since the difference between consecutive terms is not constant. Hope that helps some.
• what is an nth term??
• the variable "n" is most commonly used to symbolize ungiven numbers. any number can be represented by an "n".
• is conjectured similar to estimate?
• Sort of, but not precisely. "Sort of" because I think you are using the word estimate to mean a guess about the next value or the behavior of a sequence. Unfortunately the word estimate also means to approximate, for example by rounding a high precision answer.

A conjecture is a statement that is `likely to be true based on what you have observed` (so far), and if what you have observed so far is accurate and really, truly does represent how the phenomenon is behaving, then your statement is exactly true, not an estimate. If you are making observations and think you see a pattern, you can make a conjecture about how the next events will behave.
An example
On Monday it rained
On Tuesday it rained
On Wednesday it rained
On Thursday it rained
So, based on those events, you can make a conjecture that it will also rain on Friday.
You cannot be too surprised, though, if the storm is over and it is sunny on Friday.

That is why Sal talked about the values represented by "..." Those pieces of data may not follow the same pattern. So you can conjecture about how they will be, but you cannot definitely prove that. If they are different from what your conjecture predicted, then you need to re-examine what you know about ALL the known data and try for a new conjecture.
• at , would the sequence not be
0,3,8,63,3968,and so on?
Since it's squared and 8 squared is 64.
• what is the difference between conjecture, conclusion, and a justification
(1 vote)
• Hello Dea,

A conjecture is when a person makes a statement or proposition that seems likely to be true.
A conclusion is like a judgment or decision reached by reasoning.
A justification is like the action made by someone of showing something to be right or reasonable.
Like if someone says pencils are useless and you like pencils, you would be like no pencils are good because.... (the .... is the justification)

Hope that helps!
-JK
• I've always assumed that the "..." following a sequence implied that the pattern of the sequence continues to hold. Is this not the case? The video seems to suggest that it isn't necessarily so.
• I believe it does not necessarily mean that the pattern of the sequence continues but that the data set continues. We do not necessarily know what it continues to, we just know that there is more data.
(1 vote)
• Is there a FORMULA or an easy way for CONJECTION of more COMPLEX Situations
• No, you have to use logical reasoning to solve these kinds of problems
(1 vote)
• Is it just me or is the expression used to describe the sequence wrong? I tried calculating and it doesn't seem to work after 8.
(1 vote)
• Hi Tulsi,

The sequence matches the first six terms listed and is only supposed to fit the first six terms as we do not know what the eighth or 100th term equal to.