Systems and Sequences — Test

Question 11 • Algebra II

Which graph represents a geometric sequence?

Answer

Image with description A coordinate plane with a horizontal x-axis labeled from 1 to 9 in increments of 1 unit and a vertical y-axis labeled from 10 to 100 in increments of 10 units, with grid lines. Ten solid dots are plotted following an upward curve from left to right. Each dot is labeled with its coordinates, which are 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.

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 A coordinate plane with a horizontal x-axis labeled from 1 to 9 in increments of 1 unit and a vertical y-axis labeled from 10 to 100 in increments of 10 units, with grid lines. Ten solid dots are plotted along a straight line sloping upward from left to right. Each dot is labeled with its coordinates, which are 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.

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.

Explanation

A geometric sequence has a constant ratio between consecutive terms. In choice B, the y-values are 100, 50, 25, 12.5, and 6.25; each term is multiplied by 1/2 to get the next one. Choice C has a constant difference, which makes it arithmetic, not geometric.

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