Which sequence is best modeled by a recursive rule that multiplies by a constant?

What are the intervals where the function is less than zero? The x-axis spans from slightly below negative 2 to above 2, and the y-axis spans from below 0 to above 20. The x-axis has a scale of 2 in increments of 0.5 and the y-axis has a scale of 10 in increments of 2. The orange function exhibits multiple turning points: it starts from positive infinity, descends into a local minimum around (negative 1, 0), rises to a local maximum near (0.5, 15), dips again into another local minimum at (2, 0), and then increases steeply towards positive infinity. The curve passes through the y-axis at (0, 12). It is symmetrical around the vertical line passing through the local maximum.

The table represents a geometric sequence:   Data Table \(n\) 1 2 3 \(f(n)\) 64 16 4   Find \(\sum_{n=1}^{4} f(n)\).

A sequence is modeled by \(a_n = 7(3)^{n-1}\).   What is the value of \(a_6\)?

A sequence starts at 720 and is multiplied by \(\frac{2}{3}\) each step.   Which explicit rule models this situation?

A sequence increases by 9 each term and has \(a_1 = 7\).   What is the value of \(a_{12}\)?

A shipping company charges $15 per package. If the total cost of shipping all packages cannot exceed $300, which inequality represents the number of packages that can be shipped?

This graph shows a linear function and an absolute value function. How many solutions does the system have? “The x-axis spans from negative 5 to just above 5, and the y-axis spans from below 0 to just above 10. Both the axes have a scale of 5 in increments of 1. A solid blue V-shaped function has a sharp vertex at (3, 2) and a y-intercept of (0, 5), while the region above it is shaded in light blue. A dashed green diagonal line with a negative slope has an x-intercept at (4,0) and a y-intercept at (0,4), while the triangular region below it is shaded in light green. The blue and green shaded regions do not overlap. A white unshaded diagonal strip separates them, extending into a triangular unshaded area on the right side of the first and second quadrants. “

A geometric sequence has explicit rule \(a_n = 40(0.75)^{n-1}\). What is the sum of the first 3 terms?

How many solutions does the system represented by the parabola and absolute value graph have? The x-axis spans from below zero to just above 6, and the y-axis spans from below negative 2 to 6. Both axes have a scale of 2 in increments of 0.5.  The red parabola opens upward, with its vertex at approximately (2, negative 1), y-intercept at (0, 3), and x-intercepts at (1, 0) and (3, 0).  The green V-shaped function consists of two linear segments meeting at a sharp vertex around (3, 1), extending in opposite directions with negative and positive slopes respectively. The left segment with negative slope passes through the point (0, 4) and the right segment with positive slope passes through the point (6, 4).  The two graphs intersect at two points. The first point is roughly located halfway between x-values of 0 and negative 0.5 and y-values of 4 and 4.5. The second point is roughly halfway between x-values of 3.5 and 3.75 and y-values of 1.5 and 1.75.