Question

Can someone help me learn how to write recursive equations.

The sequence is 1,5,14,30

Answer 1

\[f _{_{1}} = 1, f _{2}= 5,\] one possible form is:
\[f _{n}=a f _{n-1}+b f _{n-2}\]

Answer 2

using \[f _{_{1}} = 1, f _{2}= 5, f_{3}=14\]
\[f _{n}=a f _{n-1}+b f _{n-2}+c f _{n-3}\]
you can write
\[f _{n}=2 f _{n-1}+0 f _{n-2}+ 2f _{n-3}\] or
\[f _{n}=1 f _{n-1}+3 f _{n-2}+ 1f _{n-3}\]

Answer 3

I am still confused the options are

an = an – 1 + n
an = an – 1 + n2
an = an – 1 + 2n
an = an – 1 + n3

Answer 4

I know that the correct answer is an=an-1+n^2
But I am not sure how to get that answer.

Answer 5

\[a _{n}=a _{n-1} +n \]

\[a _{n}=a _{n-1} +n ^{2}\]

\[a _{n}=a _{n-1} +2n\]

\[a _{n}=a _{n-1} +n ^{3}\]

I know the correct answer is

\[a _{n}=a _{n-1} +n ^{2}\]

I am just not sure how.

Answer 6

I thought if I wrote it like that it would be easier to see or understand I guess.

Answer 7

i recall something about find a homogenous and then a particular solution, but different classes on the same subject tend to go about this in different ways

Answer 8

I am not sure this even matters as far as the science goes. I think that the equation is what matters. I am still not sure how though.

Answer 9

if you are good at spotting patterns, there is a brute method you can try :)

n : 1 2 3 4 ...
an : 1 5 14 30 ...

there is no common difference or ratio that can be useful, so try some ideas; one is to square the n values and see if you can form a pattern ... which of course works since you already know the answer