If you would like to know which functions represent the arithmetic sequence 8, 1.5, -5, -11.5, ... you can find this using the following steps:
f(n) = –6.5n + 14.5 ... yes
f(1) = 8
f(2) = 1.5
f(3) = -5
f(4) = -11.5
f(n) = –1.5n + 9.5 ... no
f(1) = 8
f(2) = 6.5
f(n) = 6.5n + 1.5 ... no
f(1) = 8
f(2) = 14.5
f(1) = 8, f(n + 1) = f(n) – 6.5 ... yes
f(2) = 8 - 6.5 = 1.5
f(3) = 1.5 - 6.5 = -5
f(4) = -5 - 6.5 = -11.5
f(1) = 8, f(n + 1) = f(n) – 1.5 ... no
f(2) = 8 - 1.5 = 6.5
f(1) = 8, f(n + 1) = f(n) + 6.5 ... no
f(2) = 8 + 6.5 = 14.5
The correct result would be:
f(n) = –6.5n + 14.5 and f(1) = 8, f(n + 1) = f(n) – 6.5.
