pre-calculus sequences

[mooboodoo]

2, (-3/11), (4/26), (-5/47)...12th term

this is the sequence, it is non arithmetic and non geometric so obviously there is no formula i can use, but i have to put it in summation notation.

so far, on the bottom of the sigma i have n=1, on top i have 12, but don't know what to put to the right. so far to the right i have:

(-1)^(n-1) x (n+1/?) i am wondering if maybe this is a piecewise function, but i'm not sure.

 

[Deleted member 4993]

2, (-3/11), (4/26), (-5/47)...12th term

this is the sequence, it is non arithmetic and non geometric so obviously there is no formula i can use, but i have to put it in summation notation.

so far, on the bottom of the sigma i have n=1, on top i have 12, but don't know what to put to the right. so far to the right i have:

(-1)^(n-1) x (n+1/?) i am wondering if maybe this is a piecewise function, but i'm not sure.

a[sub:y5p7tqaj]n[/sub:y5p7tqaj] = 1/6 * n[sup:y5p7tqaj]3[/sup:y5p7tqaj] + 3/2 * n[sup:y5p7tqaj]2[/sup:y5p7tqaj] + 13/3 * n - 5

 

[mooboodoo]

I'm not quite sure that this works; can you plug in a value for n and show me? I tried doing this but I couldn't get it to work

 

[galactus]

Plug in a value for you?. Surely you have a calculator.

Google the 'Method of Finite Differences' and you can see how it is derived.

There is a pattern ot the numbers.

\(\displaystyle 1 \;\ \;\ 11 \;\ \;\ 26 \;\ \;\ 47\)

\(\displaystyle \;\ 10 \;\ \;\ 15 \;\ \;\ 21\)

\(\displaystyle \;\ \;\ \;\ 5 \;\ \;\ 6\)

\(\displaystyle \;\ \;\ \;\ \;\ \;\ 1\;\ \;\\)

See how it eventually resolves to 1 at the bottom?. There is a pattern. It is a cubic because there are 3 rows not counting the 1 at the bottom.

 

[mooboodoo]

thank you!

 

[soroban]

Hello, mooboodoo!

\(\displaystyle 2,\;-\frac{3}{11},\; \frac{4}{26},\;-\frac{5}{47},\;\hdots \;12^{th}\text{ term}\)

\(\displaystyle \text{I agree . . . The numerator is: }\-1)^{n+1}(n+1)\)


\(\displaystyle \text{The denominator seems to be a cubic: }\;1,\;11,\;26,\;47,\hdots\)
. . \(\displaystyle \text{which is generated by: }\:\tfrac{1}{6}(n^3 + 9n^2 + 26n - 30)\)


Edit: Ah, galactus beat me to it . . .
.

 

[mooboodoo]

Thank you soroban and galactus, I finally understand!!!!

 

[mooboodoo]

soroban-or anyone else-how did you get that equation? it works, but just wondering?