Question

1, 8, 27, 64, ...

What are the next 3 numbers in the sequence and how do I figure them out?

Answer 1

It's a pattern...... I guess I'd suggest just looking at it a bit longer and giving it some thought.

Answer 2

every term is x^3

You have:

1^3, 2^3, 3^3, 4^3, ...

So, the next 3 would be:

5^3, 6^3, 7^3

or

125, 216, 343

Answer 3

All good now @xbrittxcheerx92x ?

Answer 4

I still don't really understand how you did this problem :(

Answer 5

The key is starting by associating the number 1 with the first term, the number 2 with the second term, 3 with the 3rd, 4 with the 4th and seeing if for any of them (I'd look at terms 2,3,4) have a relationship with the number of the term and its value.

for instance, trying to find a relationship between 4 and 64 or between 3 and 27. If you look at 2 of them together like this, you'll see that they are cubes.

Answer 6

Because 3 x 3 x 3 = 27

and 4 x 4 x 4 = 64

and 2 x 2 x 2 = 8

same for 1

Answer 7

So each term in the sequence is just that number cubed.

Answer 8

It helps if you write the position under each number in the sequence:

1 8 27 64
1 2 3 4

That's an effective visual aid.

Answer 9

Oh! ok. I get it now. Thanks :)

Answer 10

So, the end result:

1 8 27 64 125 216 343
1^3 2^3 3^3 4^3 5^3 6^3 7^3
1 2 3 4 5 6 7

Answer 11

If I graphed y = x^3, would you like to see that? That also is a good visual aid. @xbrittxcheerx92x

Answer 12

This can help:

Answer 13

Thank you so much!

Can you help me out with another equation please?

Answer 14

ok! Don't forget to medal!

Answer 15

1, 12, 123, 1234, 12345, ...

Answer 16

That one is a quirky type of sequence. You just put the next number after the end of each number. Notice how the 3rd term has a "3" put after the "12"

Answer 17

And then for the 4th term, a "4" is put after the "123" which is the 3rd term. It's like building blocks or stacking.

Answer 18

Mathematically, you could say the rule to get a term is just to take the previous term, multiply it by 10, and then add the positional number of the term to that product.

For instance:

The 7th term is 10 times the 6th term plus 7 or 123456 x 10 + 7

Answer 19

Making sense now @xbrittxcheerx92x ?

Answer 20

yes. Thank you so much!

Answer 21

Good luck in all of your studies and thx for the recognition! @xbrittxcheerx92x

Answer 22

No problem. Thank you! :)