What is the closed form equation that will generate the sequence:

{3,6,11,18,27,38,51,66,...}

An = ?

Question

What is the closed form equation that will generate the sequence:

{3,6,11,18,27,38,51,66,...}

An = ?

amistre64 · Answer

so far so good

amistre64 · Answer

yes, its adding 2n+1 to the previous terms

anonymous · Answer

if you start with 1 you just get n^2

anonymous · Answer

so somehow we have to adjust

amistre64 · Answer

teacher couldnt figure it out, so i got extra credit for it when i schooled her ;)  lol

anonymous · Answer

so is it just n^2 + 2?

amistre64 · Answer

thats it

anonymous · Answer

oh that wasn't so bad...

amistre64 · Answer

\begin{array}c
\
3&=3+0\
6&=3+3\
11&=3+8\
18&=3+15\
27&=3+24\
38&=3+35\
etc...&...\
\end{array}

if we can add 1 to the right we got the perfect squares; so i borrowed one from the left to get:  2 + n^2

amistre64 · Answer

after getting a 91 on the proofs exam, i decided to jump on the extra credit ;)