Answer:
[tex]\text{C. f(x)} = 3(1.5)^{x-1}[/tex]
Step-by-step explanation:
The numbers don’t increase by a constant amount, so this is not an arithmetic sequence.
It appears to be a geometric sequence.
The general formula for each term in a geometric sequence is
aₙ = a₁rⁿ⁻¹
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Calculate the value of r
You can calculate the r-value by dividing any two consecutive terms in the sequence.
rₙ = aₙ/aₙ₋₁
a₂/a₁ = 4.5/3 = 1.5
a₃/a₂ = 6.75/4.5 = 1.5
a₄/a₃ = 10.125/6.75 = 1.5
a₅/a₄ = 15.1875/10.125 = 1.5
r = 1.5
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Determine the formula for the nth term
a₁ = 3; r = 1.5 Substitute the values
aₙ = 3(1.5)ⁿ⁻¹ Write the equation as a function of x
[tex]\text{f(x)} = 3(1.5)^{x-1}[/tex]
