Recursive Formula Help, and Expansion of a sequence...

[Idealistic]

I'm having trouble finding a recursive formula for this sequence:

4, 7, 2, 13, 22, 37, 72, 131, 240

I came up with this lol: t(n) = t(n-1) + [t(n) - t(n-1)] until I realised that this could work for any sequence, and its wrong becuase the formula uses t(n) in it.

Also, All I need to know is if this is right:

10
∑ n/n+1
n=3

3/4, 4/5, 5/6, 6/7, 7/8, 8/9, 9/10, 10/11

I appreciate any help.

 

[royhaas]

Add the first three terms of the sequence.

For the second problem, your notation indicates you sould add those terms.

 

[Idealistic]

Add the first three terms of the sequence.

For the second problem, your notation indicates you sould add those terms.

Oh no, I'm not looking for the total sum, I just need to expand it.

 

[pka]

Here is what Prof Haas meant.
\(\displaystyle \L t_1 = 4,\;t_2 = 7,\;t_3 = 2,\;\left( {n \ge 4} \right)\left[ {t_n = t_{n - 1} + t_{n - 2} + t_{n - 3} } \right]\)

 

[soroban]

Hello, Idealistic!

I'm having trouble finding a recursive formula for this sequence:
. . 4, 7, 2, 13, 22, 37, 72, 131, 240

After the first three terms, each term is the sum of the three preceding terms.

\(\displaystyle \begin{array}{ccc}13 & = & 2\,+\,7\,+\,4 \\ 22 & = & 13\,+\,2\,+\,7 \\ 37 & = & 22\,+\,13\,+\,2 \\ 72 & = & 37\,+\,22\,+\,13 \\ 131 & = & 72\,+\,37\,+\,22
\\ 240 & = & 131\,+\,72\,+\,37 \end{array}\)

Hence: \(\displaystyle \:t_n \;=\;t_{n-1}\,+\,t_{n-2}\,+\,t_{n-3}\;\) for \(\displaystyle n\,\geq\,4\)

Ha! . . . pka beat me to it . . .

 

[pka]

Ha! . . . pka beat me to it . . .

Only by a day and a half!