Question

How would you find the nth term for a sequence like this? 1,5,11,19,29,41.
I know that the difference between the numbers increase by 2 each time, 4, 6, 8, 10, 12. None of the formulas I have tried are working

Answer 1

Hint:
fit a parabola through the given points
f(n)=an^2+bn+c
f(1)=1
f(2)=5
f(3)=11
Solve for a,b and c and you'll get the function f(n) which calculates the nth term directly.

Answer 2

Honestly that just made me more confused.

Answer 3

Do you need to find the nth term for any value of n, or just n=11, for example?

Answer 4

I have to find the nth term for any value of N. So I just need to find a formula but I don't know where to really start with it

Answer 5

Have you solved quadratic equations before?

Answer 6

I did in high school but that was 2 years ago. I really don't know

Answer 7

You'll need your high-school math skills if you want to continue with maths.
Maths is a cumulative knowledge. I quote someone else who said if you skip some basic skills, it's like climbing a ladder with the bottom rungs missing.

Answer 8

You'll also need to solve a system of 3 equations.
Short of all that, you can find your answer by trial and error, but that could take you a long time (or you can hit the right answer in 5 minutes).

Answer 9

The simplest way (short of trial and error) is to assume a parabola with coefficients a, b and c:
f(n)=an^2+bn+c
since we know the first three terms, we form three equations, substituting n=1, 2 and 3:

f(1)=1=a+b+c
f(2)=5=4a+2b+c
f(3)=11=9a+3b+c
Solving the three equations, we get a=1, b=1, c=-1, so

f(n)=n^2+n-1

will let you calculate the nth term of the series for any integer n.