Chapter 15

Evaluate each sum using a formula for \(S_{n}\). $$\sum_{i=1}^{18}(3 i-11)$$

The number of bacteria in a culture doubles every day. If a culture begins with 1000 bacteria, how many bacteria are present after 7 days?

Evaluate each sum using a formula for \(S_{n}\). $$\sum_{i=1}^{215}(i-10)$$

Find the sum of the terms of the infinite geometric sequence, if possible. $$a_{1}=8, r=\frac{1}{4}$$

Find the sum of the terms of the infinite geometric sequence, if possible. $$a_{1}=18, r=\frac{1}{3}$$

Evaluate each sum using a formula for \(S_{n}\). $$\sum_{i=1}^{100}\left(\frac{1}{2} i+6\right)$$

Find the sum of the terms of the infinite geometric sequence, if possible. $$a_{1}=5, r=-\frac{4}{5}$$

This month Warren deposited \(\$ 1500\) into a bank account. He will deposit \(\$ 100\) into the account at the beginning of each month. Disregarding interest, how much money will Warren have saved after 9 months?

Find the sum of the terms of the infinite geometric sequence, if possible. $$a_{1}=20, r=-\frac{3}{4}$$

Solve each application. When Antoinnette is hired for a job, she signs a contract for a salary of \(\$ 34,000\) plus a raise of \(\$ 1800\) each year for the next 4 yr. What will be her salary in the last year of her contract?

Find the sum of the terms of the infinite geometric sequence, if possible. $$a_{1}=3, r=\frac{3}{2}$$

Find the sum of the terms of the infinite geometric sequence, if possible. $$8, \frac{16}{3}, \frac{32}{9}, \frac{64}{27}, \dots$$

Solve each application. A stack of logs has 12 logs in the bottom row, (the first row 11 logs in the second row, 10 logs in the third row, and so on, until the last row contains one log. a) How many logs are in the eighth row? b) How many logs are in the stack?

Find the sum of the terms of the infinite geometric sequence, if possible. $$\frac{7}{2}, \frac{7}{4}, \frac{7}{8}, \frac{7}{16}, \dots$$

A landscaper plans to put a pyramid design in a brick patio so that the bottom row of the pyramid contains 9 bricks and every row above it contains two fewer bricks. How many bricks does she need to make the design?

A lecture hall has 14 rows. The first row has 12 seats, and each row after that has 2 more seats than the previous row. How many seats are in the last row? How many seats are in the lecture hall?

Find the sum of the terms of the infinite geometric sequence, if possible. $$-12,8,-\frac{16}{3}, \frac{32}{9}, \dots$$

A theater has 23 rows. The first row contains 10 seats, the next row has 12 seats, the next row has 14 seats, and so on. How many scats are in the last row? How many seats are in the theater?

The main floor of a concert hall seats 860 people. The first row contains 24 seats, and the last row contains 62 seats. If each row has 2 more seats than the previous row, how many rows of seats are on the main floor of the concert hall?

Find the sum of the terms of the infinite geometric sequence, if possible. $$36,6,1, \frac{1}{6}, \dots$$

A child builds a tower with blocks so that the bottom row contains 9 blocks and the top row contains 1 block. If he uses 45 blocks, how many rows are in the tower?

Find the sum of the terms of the infinite geometric sequence, if possible. $$-40,-30,-\frac{45}{2},-\frac{135}{8}, \dots$$

Find the sum of the terms of the infinite geometric sequence, if possible. $$4,-12,36,-108, \dots$$

Each time a certain pendulum swings, it travels \(75 \%\) of the distance it traveled on the previous swing. If it travels \(3 \mathrm{ft}\) on its first swing, find the total distance the pendulum travels before coming to rest.

Each time a certain pendulum swings, it travels \(70 \%\) of the distance it traveled on the previous swing. If it travels 42 in, on its first swing, find the total distance the pendulum travels before coming to rest.

A ball is dropped from a height of 27 ft. Each time the ball bounces it rebounds to \(\frac{2}{3}\) of its previous height. a) Find the height the ball reaches after the fifth bounce. b) Find the total vertical distance the ball has traveled when it comes to rest. (GRAPH CANT COPY)

A ball is dropped from a height of 16 ft. Each time the ball bounces it rebounds to \(\frac{3}{4}\) of its previous height. a) Find the height the ball reaches after the fourth bounce. b) Find the total vertical distance the ball has traveled when it comes to rest.