A sequence has \(a_1 = -12\) and common difference \(6\).   What is the value of \(a_{11}\)?

A sequence begins with \(a_1 = 900\) and increases by 12% each step.   Which recursive rule models this situation?

A geometric sequence has first term \(a_1 = 64\) and common ratio \(\frac{1}{4}\). Which explicit rule models this sequence?

Find the sum of the infinite series   \(\sum_{n=1}^{\infty} 15\left(\frac{1}{3}\right)^{n-1}\).

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 \(a_{12}\)?