Determine the most probable next term in the list of numbers. Show work to support your answer.

Question

280, 480, 684, 913, 1205, 1615, …

Answer 1

Set of known values:

x = 1 , y = 280

x = 2 , y = 480

x = 3 , y = 684

x = 4 , y = 913

x = 5 , y = 1205

x = 6 , y = 1615

The interpolating polynomial is :

y = ( 17 x ^ 4 - 86 x ^ 3 + 139 x ^ 2 + 4730 x + 1920 ) / 24

For x = 7 , y = 2215

Next term :

2215