Which of the following graphs could be a representation of a geometric sequence? Check all that apply
2 answers:
Answer:
Step-by-step explanation:
The formula for a geometric series is aₙ = a₁rⁿ⁻¹.
This is analogous to the exponential series y = a₀rⁿ.
The difference it that, in a geometric series, n must be positive.
Thus, the graph of a geometric series starts somewhere on the y-axis and either increases exponentially or decreases asymptotically to the x axis.
In Graph A , the successive values of y are 5/2⁰, 5/2¹, 5/2² and 5/2³. This is an example of exponential decay.
In Graph B, the successive values of y are 3¹, 3² and 3³. This is an example of exponential growth.
In Graph C, the successive values of y are 2¹, 2², 2³, and 2⁴, another example of exponential growth.
In Graph D, the successive values of y are 1, 2.5, 4, 5.5. and 7. There is a constant difference of 1,5, so this represents an arithmetic series.
could represent a geometric series.
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