How to find the nth term of this sequence

-11, -13, 7, 61, 161

I've solved one part of the question, which is that the numbers have a relation of 12. But after that im lost.

Question

How to find the nth term of this sequence

-11, -13, 7, 61, 161

I've solved one part of the question, which is that the numbers have a relation of 12. But after that im lost.

vecters · Answer

-12*

welshfella · Answer

what do you mean by they have a relation of -12?

vecters · Answer

sorry i actually meant 12, made a calculation mistake.

What i mean is that when simplified, the pattern gives a result of 12

welshfella · Answer

Im afraid I don't follow that..
Simplified?

vecters · Answer

hopefully this will explain it better, sorry for bad drawing.

vecters · Answer

Hopefully that was readable

welshfella · Answer

yes

vecters · Answer

so what would be the answer

welshfella · Answer

I cant figur out this one 
Lets see if its on the encyclopoedia of series

welshfella · Answer

https://oeis.org/search?q=-11%2C-13%2C7%2C61%2C161&language=english&go=Search Nope

vecters · Answer

So is it not possible to solve?

welshfella · Answer

maybe

welshfella · Answer

But because its not on the list doesn't mean its impossible.

vecters · Answer

i have an idea, but i dont know if it is correct, but we were learning quadratic sequences in class so this could be quadratic sequence and the quadratic formula for this sequence could be an^3 + bn^2 + cn + d

Does this make sense? im new to this topic

vecters · Answer

@welshfella

jango_in_dtown · Answer

Ok I have a solution

jango_in_dtown · Answer

we will do it by newton's forward interpolation formula..

vecters · Answer

uhmm okay, but please keep in mind that i am in 9th standard so hopefully the formula isnt too complicated

jango_in_dtown · Answer

the general formula, will be 2(n-1)(x-2)(x-3)+11(n-1)(n-2)-2x-9

jango_in_dtown · Answer

oh.. replace those x by n

jango_in_dtown · Answer

f(n)=2(n-1)(n-2)(n-3)+11(n-1)(n-2)-2n-9

jango_in_dtown · Answer

check if the values are correct or not... put n=1, n=2, etc

vecters · Answer

ok i will try it, thanks for the help!

jango_in_dtown · Answer

will you not learn how I got it?

welshfella · Answer

I've never heard of tht newton formula. Must look it up.

jango_in_dtown · Answer

But check , I got the formula right, just put the values @welshfella

welshfella · Answer

it works for n = 1,2 and 3  - giving -11,-13 and 7

jango_in_dtown · Answer

check kor n=4 and 5 also

welshfella · Answer

im going too now

welshfella · Answer

works for n = 4

welshfella · Answer

Yes also for n = 5

welshfella · Answer

good job