Question

Negative 2 and two-thirds, negative 5 and one-third, negative 10 and two-thirds, negative 21 and one-third, negative 42 and two-thirds, ellipsis
Which formula can be used to describe the sequence?

f(x + 1) = –2f(x)
f(x + 1) = Negative one-halff(x)
f(x + 1) = One-halff(x)
f(x + 1) = 2f(x)

Answer 1

Convert to improper fractions: -2 2/3 = -8/3, -5 1/3 = -16/3, -10 2/3 = -32/3, -21 1/3 = -64/3, -42 2/3 = -128/3.
Each term is twice the previous term (e.g. (-16/3)/(-8/3) = 2), so the recurrence is

f(x + 1) = 2 f(x).