Calculus polynomial

Question

Use polynomial fitting to find the formula for the nth term of the sequence (an)n≥0

 0,1,7,21,46,85,... 

Use polynomial fitting to find the formula for the nth term of the sequence (an)n≥0

 2,3,7,15,28,47,...

Answer 1

If you have a TI-84, you can put the following in a list:

L₁ L₂

1 0

2 1

3 7

4 21

5 46

6 85

Then ensure your diagnostics are turned on (if you don't know how, google it)

Then use "stat" "CALC" and start with "5:QuadReg" and look for an R² = 1 which will be a perfect fit. If you don't get it, do "stat" "CALC" and "6:CubicReg" and again, if you don't get R² = 1, do "stat" "CALC" and "7:QuartReg". If that doesn't work, you'll need to use desmos or equivalent for higher orders of polynomials.

I got R² = 1 on a cubic for this problem. Once you get it, create the polynomial with the coefficients your calculator tells you and make the function in terms of "n" instead of "x"