Topic: Inductive Reasoning.

[Wilder]

How many matches are there? If those numbers can't be seen, here they're: 1, 2, 3, 19 and 20. Also, there are 5 matches per figure.

 

[lev888]

How many matches are there? If those numbers can't be seen, here they're: 1, 2, 3, 19 and 20. Also, there are 5 matches per figure.

Where are you stuck?

 

[Wilder]

Where are you stuck?

The column 1, 2, 3 must equal 5, 15, 30, respectively, by performing same operation per row. E.g. 5=5(1²) 15≠5(2²) 30≠5(3²)

 

[lev888]

The column 1, 2, 3 must equal 5, 15, 30, respectively, by performing same operation per row. E.g. 5=5(1²) 15≠5(2²) 30≠5(3²)

I don't understand the above.
Do you see that we can start by counting the number of 5s, not matches? Let's say it's N. Then the total number of matches will be what?
Now, how do we count 5s?
How many 5s in the first row? Second? etc. See a pattern? Do you know how to calculate the sum of such sequence of numbers?

 

[Wilder]

Replies to your questions.
Yes, I do. That's the question. By forming triangles. 20. 19. Nth row: 1. Yes. To be honest, no. That's why I came here.

Do you know how?

 

[Dr.Peterson]

You mention triangles. Do you know about triangular numbers? If so, that's what you use. If not, you can look it up, or we can explain it.

It can also be explained in terms of arithmetic series, if you know about that.

I'm also curious about your calling this "inductive reasoning", which suggests a possible context. What have you been learning that might be of use here?

 

[lev888]

Replies to your questions.
Yes, I do. That's the question. By forming triangles. 20. 19. Nth row: 1. Yes. To be honest, no. That's why I came here.

Do you know how?

Mathwords: Arithmetic Series

---

www.mathwords.com

 

[Steven G]

I am missing something. The 1st row has three layers of 5, but the 20th row only has two lowers of 5. How can that be? Where does it change from three layers to two layers?

 

[lev888]

The 1st row has three layers of 5

I think it's the first 3 rows, not the 1st row. Each row has one layer.

 

[Dr.Peterson]

I am missing something. The 1st row has three layers of 5, but the 20th row only has two lowers of 5. How can that be? Where does it change from three layers to two layers?

I think each row is a single row. We are shown the first three and the last two rows. And Wilder is calling each row a "column".

 

[Wilder]

You mention triangles. Do you know about triangular numbers? If so, that's what you use. If not, you can look it up, or we can explain it.

It can also be explained in terms of arithmetic series, if you know about that.

I'm also curious about your calling this "inductive reasoning", which suggests a possible context. What have you been learning that might be of use here?

This could help a lot.

 

[Steven G]

How many 5's are there.
row 1 has 1
row 2 has 2
row 3 has 3
...
row 20 has 20.

So how many 5's are there? If each 5 has 5 sticks then how many sticks are there in total?

 

[Dr.Peterson]

This could help a lot.

Are you saying that this is an example you were given, to show what you have been learning?

It looks like you are expected just to guess at a pattern, and just confirm it (as far as you can) by testing additional cases (that might be the inductive reasoning). But with no words of explanation, I can't see what they are counting, as the first example doesn't have 2 of anything.

I do see why you seem to have made a bad guess in your post #3. Don't just imitate what they said; do (in some sense) what they did!

But you can just do what Jomo suggested in post #12, without needing a formula!