Modeling with Sequences and Series — Test

Question 13 • Precalculus

Which graph represents a geometric sequence?

Answer

Image with description On the coordinate plane, the x axis is marked from 0 to 10 with an interval of 1 unit and the y axis is marked from 0 to 100 with an interval of 10 units. The points (0 comma 100), (1 comma 50), (2 comma 25), (3 comma 12 point 5), and (4 comma 6 point 25) are plotted on the graph. The points are labeled on the graph with the coordinates.

Image with description On the coordinate plane, the x axis is marked from 0 to 10 with an interval of 1 unit and the y axis is marked from 0 to 100 with an interval of 10 units. The points (0 comma 0), (1 comma 1), (2 comma 4), (3 comma 9), (4 comma 16), (5 comma 25), (6 comma 36), (7 comma 49), (8 comma 64), and (9 comma 81) are plotted on the graph. The points are labeled on the graph with the coordinates.

Image with description On the coordinate plane, the x axis is marked from 0 to 10 with an interval of 1 unit and the y axis is marked from 0 to 100 with an interval of 10 units. The points (0 comma 100), (1 comma 50), and (2 comma 0) are plotted on the graph. The points are labeled on the graph with the coordinates.

Image with description On the coordinate plane, the x axis is marked from 0 to 10 with an interval of 1 unit and the y axis is marked from 0 to 100 with an interval of 10 units. The points (0 comma 0), (1 comma 10), (2 comma 20), (3 comma 30), (4 comma 40), (5 comma 50), (6 comma 60), (7 comma 70), (8 comma 80), and (9 comma 90) are plotted on the graph. The points are labeled on the graph with the coordinates.

Explanation

A geometric sequence has the same ratio between each consecutive pair of terms. In graph D, the y-values go from 100 to 50 to 25 to 12.5 to 6.25, so each value is multiplied by 1/2 to get the next one. Therefore, graph D represents a geometric sequence.

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