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QuizMultiple Choice

Geometric Sequences — Quiz

Question 1 • Algebra: Concepts and Connections

negative 81 comma 108 comma negative 144 comma 192 comma dot dot dot Which formula can be used to describe the sequence?

Answer
A
f of x is equal to negative 81 times 3 fourths raised to the x minus 1 power
B
f of x is equal to negative 81 times open paren negative 4 thirds close paren raised to the x minus 1 power
C
f of x is equal to negative 81 times 4 thirds raised to the x minus 1 power
D
f of x is equal to negative 81 times open paren negative 3 fourths close paren raised to the x minus 1 power

Explanation

The sequence is geometric because each term is multiplied by the same ratio: 108 ÷ (−81) = −4/3, and −144 ÷ 108 = −4/3. A geometric sequence has formula f(x) = first term × ratio^(x − 1). Using first term −81 and ratio −4/3 gives f(x) = −81(−4/3)^(x − 1), which is choice B.

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