Question

–81, 108, –144, 192, ...

Which formula can be used to describe the sequence?

f(x) = –81(four-thirds) Superscript x minus 1
f(x) = –81(negative three-fourths) Superscript x minus 1
f(x) = –81(negative four-thirds) Superscript x minus 1
f(x) = –81(three-fourths) Superscript x minus 1

Answer 1

f(x) = −81(−4/3)^(x−1)

Reason: each term is multiplied by −4/3 to get the next (−81 → 108 multiplies by −4/3, and magnitudes increase by 4/3), so the geometric formula is a1( r )^(x−1) with a1 = −81 and r = −4/3.