Question

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

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

An = ?

Answer 1

so far so good

Answer 2

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

Answer 3

if you start with 1 you just get n^2

Answer 4

so somehow we have to adjust

Answer 5

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

Answer 6

so is it just n^2 + 2?

Answer 7

thats it

Answer 8

oh that wasn't so bad...

Answer 9

\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

Answer 10

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