Question

Which formula can be used to describe the sequence?

Negative two-thirds, −4, −24, −144,...

f(x) = 6(negative two-thirds) Superscript x minus 1
f(x) = −6(Two-thirds) Superscript x minus 1
f(x) = Negative two-thirds(6)x − 1
f(x) = Two-thirds(−6)x − 1

Answer 1

The sequence is geometric with first term a1 = −2/3 and common ratio r = 6, so

f(x) = (−2/3)·6^(x−1).

(That is option 3. The other choices give the wrong sign or wrong first term.)