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

Lesson 9: Deductive and inductive reasoning

# Using inductive reasoning

Sal uses inductive reasoning to find an expression for the nth number in the sequence 6, 9, 12, 15,.... Created by Sal Khan.

## Want to join the conversation?

• I thought about (3 (n - 1)) + 6.
• That is because when you expand 3(n - 1) + 6, you get 3n - 3 + 6 which is equal to 3n + 3. That is the same as 3(n + 1) = 3n + 3.
• what does "nth" number mean?
• It's like a stand-in for any number... so a variable. If that shortens things. :-)
• Isn't this reasoning deductive? Couldn't we say that Sal "proved" that the nth term is 3n+3? To put it in another way: how can we say that Sal conjectured that the Nth term is 3n+3?
• It is inductive because it is based upon observing the pattern in the given numbers. Conclusions based on observations are inductive. Sal to specific observations and used them to draw a general conclusions.

Deductive reasoning is when you start with a general rule(s) and you draw a specific conclusion.

Hope this helps.
• Why are simple math concepts such as skip counting involved in precalculus?
• And arithmetic progressions(AP) where the difference between two consecutive terms are constant, such as:10,15,20,25....
Then to find out the nth term of an AP where the first term is 'a' and the constant difference is 'd' then the "n"th term is : a+(n-1)*d.
Finding the sum is easy also like: when "n" is the number of terms, 'I' is the first term and "F" is the final term, the sum is :
[n(I+F)]/2
• Why is 3n+3 the right anwser while the pattern is adding by 3 so wouldn't n+3 work too?
• what is the next number, 64,-16,4,-1,__
• 1/4, as each subsequent number in the series is a square of half the previous number's square root, alternatively positive, then negative.
• What does nth mean is that a number?
(1 vote)
• When we are working with sequences (and series), we care about the value of each term AND the number of the term. In the following sequence, the first term has a value of 4 and n=1
The second term has a value of 6 and n=2 (the number of the term is 2)
The nth term means the term with a number of n. If n=2, we are asking for the second term. If n = 6, we are asking for the nth term, which I did not give below. You can write a formula to allow you to tell me any value if I give you any value of n.
Here is the sequence: 4 6 8 10 12 ...
`Term 1 = 4` n = 1
`Term 2 = 6` n = 2
`Term 3 = 8` n = 3
etc.
You can build a formula to tell what other values of terms would be.
a_n = amount you want to find out `nth term`
a₁ = first amount or amount of the first term which was 4
d = common difference which was 6 - 4 = 2
a_n = a₁ + d(n-1) → formula for `nth term` if it is arithmetic
a_n = 4 + 2(n-1) → formula for `nth term`

Or we can say that a_n = 2n + 2
(the same thing as the other formula, but simplified)

So, if I want the 50th term (n = 50)
a_50 = 4 + 2(50 - 1) = 4 + 98 = 102
With the other formula, a_n = 2n + 2 = 2∙50 + 2 = 102
a_50 = 102

As you study sequences and series, you will see that there are many kinds of sequences--this is just a very simple example.
(1 vote)
• There used to be some really nice assignments/ practice that went w. deductive reasoning ("logical arguments and deductive reasoning" was the name)a couple years ago. Is this content still available elsewhere? It helped my students to iron out their issues.
(1 vote)
• When they restructured the menus, they left some content stranded (not on any menu). I have found items using the search bar even when they aren't on a menu. Give it a try and see if you can find the assignments/videos that you want.
(1 vote)
• I still don't understand why you have to add one from the term to the number.
(1 vote)
• What will be the next number for these sequence 9,4,3,12,37,84,_ ?
(1 vote)