Question

What is the next number in the pattern?
1,-4,9,-16...

Answer 1

Notice how 1, 4, 9, 16 is the list of the first four perfect squares

1 = 1^2
4 = 2^2
9 = 3^2
16 = 4^2

Answer 2

the only difference is that you are alternating in sign for each term

Answer 3

so it grows by multiplication?

Answer 4

the rule for generating perfect squares is n^2 where n is a positive whole number

the rule for your sequence is (-1)^(n+1)*n^2, again n is a positive whole number

the (-1)^(n+1) portion helps you get the correct sign for each term

Answer 5

i dont really understand.... im sorry

Answer 6

have you learned about perfect squares?

Answer 7

no not really i had a virtual class and they didnt really go into that topic

Answer 8

have you learned about squaring numbers?

Answer 9

ummm... can you give me an example of squaring numbers? it sounds familiar

Answer 10

squaring means you multiply a number by itself

Answer 11

it comes from the idea that the area of a square is (side)*(side)

Answer 12

example

9^2 = 9*9 = 81

area of a square with side length of 9 is 9*9 = 81

Answer 13

yes i understand that and i have learned it

Answer 14

so what is 5^2

Answer 15

25

Answer 16

how about 6^2

Answer 17

36

Answer 18

so,

1 = 1^2
4 = 2^2
9 = 3^2
16 = 4^2

agreed?

Answer 19

yes

Answer 20

1,4,9,16 are a list of perfect squares

they are the first 4 perfect squares (squaring the first four positive whole numbers)

Answer 21

the next perfect square is 25 since 5^2 = 25

Answer 22

we have this list now: 1, 4, 9, 16, 25

Answer 23

let's go back to 1,-4,9,-16...

Answer 24

the difference between 1,-4,9,-16... and 1, 4, 9, 16,... is that the signs are alternating

Answer 25

yeah

Answer 26

so the next term is 25

1,-4,9,-16, 25

and the next term is -36

1,-4,9,-16, 25, -36

etc etc

Answer 27

yes it makes sense thank you very much

Answer 28

you're welcome