Soroban
Posts:
77
Registered:
12/6/04


how do i find the nth term?
Posted:
Jan 20, 2004 12:31 PM


Hello, Laura!
>I'm really stuck on this sequence of numbers; 5, 20, 50, 100, 175, 280, >and how to find the formula for the nth term. Please can anybody enlighten me?!
Taking consecutive differences, we get: 15, 30, 50, 75, 105, ... Taking differences again: 15, 20, 25, 30, ... Taking differences again: 5, 5, 5, ...
The third differences are constant. Hence, the function is a CUBIC of the form: f(n) = an^3 + bn^2 + cn + d
We know the first four values of this function: f(1) = 5, f(2) = 20, f(3) = 50, f(4) = 100
Plugging those values into the general form, we get: f(4) = 64a + 16b + 4c + d = 100 f(3) = 27a + 9b + 3c + d = 50 f(2) = 8a + 4b + 2c + d = 30 f(1) = a + b + c + d = 5
Solving this system, we get: a = 5/6, b = 5/2, c = 5/3, d = 0
The function is: f(n) = (5/6)n^3 + (5/2)n^2 + (5/3)n = 5n(n + 1)(n + 2)/6

