91Ó°ÊÓ

Determine whether each infinite geometric series converges or diverges. If it converges, find its sum. $$ 8+4+2+\cdots $$

Graph the system of inequalities. Tell whether the graph is bounded or unbounded, and label the corner points. $$ \left\\{\begin{array}{r} x \geq 0 \\ y \geq 0 \\ x+y \leq 6 \\ 2 x+y \leq 10 \end{array}\right. $$

Find \(x\) so that \(x+3,2 x+1,\) and \(5 x+2\) are consecutive terms of an arithmetic sequence.

Determine whether each infinite geometric series converges or diverges. If it converges, find its sum. $$ 2-\frac{1}{2}+\frac{1}{8}-\frac{1}{32}+\cdots $$

If \(y=\frac{5}{3} x^{3}+2 x+C\) and \(y=5\) when \(x=3,\) find the value of \(C\).

How many terms must be added in an arithmetic sequence whose first term is 11 and whose common difference is 3 to obtain a sum of \(1092 ?\)

Determine whether each infinite geometric series converges or diverges. If it converges, find its sum. $$ \sum_{k=1}^{\infty} 5\left(\frac{1}{4}\right)^{k-1} $$

Seats in an Amphitheater An outdoor amphitheater has 35 seats in the first row, 37 in the second row, 39 in the third row, and so on. There are 27 rows altogether. How many can the amphitheater seat?

Football Stadium The corner section of a football stadium has 15 seats in the first row and 40 rows in all. Each successive row contains two additional seats. How many seats are in this section?

Determine whether each infinite geometric series converges or diverges. If it converges, find its sum. $$ \sum_{k=1}^{\infty} 4\left(-\frac{1}{2}\right)^{k-1} $$