Question

write a recursive definition for each sequence.-2,7,16,25

Answer 1

help me please @whpalmer4

Answer 2

pick any term and subtract the previous term

what difference do you get?

Answer 3

positive 9

Answer 4

so we're adding 9 to each term to get the next term

Answer 5

yes

Answer 6

-2 + 9 = 7
7+9 = 16
16+9 = 25

Answer 7

How do you generalize this?

Answer 8

im not sure. are you asking for a equation?

Answer 9

what's the rule to get the next term?

Answer 10

how do I find the term after 25?

Answer 11

you will add 9 to 25.

Answer 12

so say you want to find the nth term, what's the rule to do this?

Answer 13

will it be n+9

Answer 14

close

Answer 15

actually it will be

\[\Large a_{n-1} + 9\]

where \(\Large a_{n-1}\) is the term just before the nth term

Answer 16

so

\[\Large a_{n} = a_{n-1} + 9\]

Answer 17

This basically says

nth term = (term right before the nth term) + 9

Answer 18

and that's how recursion works in this case

Answer 19

i dont know what that is??? o.0

Answer 20

you've never seen that notation before?

Answer 21

maybe you've seen it as a(n) and a(n-1) ??

Answer 22

ok that looks more like what i know. yes i do know what it is.

Answer 23

ok so it would be

a(n) = a(n-1) + 9

which translates to

nth term = (term right before the nth term) + 9

Answer 24

So if you wanted to know the 55th term for instance, then you would have to know the 54th term. To know the 54th term, you'd have to know the 53rd term, etc etc. So you can see that it's a lot of work using recursion.

Answer 25

yes i do. i get it now thank you for you time :D

Answer 26

you're welcome