Sequences and Series Word Problems

 A display of cans on a grocery shelf consists of 200 cans on the bottom, 194 cans in the next row, and so on in an arithmetic sequence, until the top row has 14 cans.  How many cans, in total, are in the display?

• 2800 cans

• 6848 cans

• 1498 cans

• 3424 cans

A coach wants to determine the seating capacity of a gymnasium with 18 seats on the first row, 20 on the second, 22 on the third. The sequence of the seating capacity per row continues until the 14th row. The proper formula to use based on this description is ___________________ .

• Arithmetic Sequence

• Arithmetic Series

• Geometric Sequence

• Geometric Series

A tennis ball bounces on the ground 𝑛 times. The heights of the bounces, ℎ1,ℎ2,ℎ3,…,ℎ𝑛​, form a geometric sequence. The height that the ball bounces the first time, ℎ1​, is 80 cm, and the second time, ℎ2​, is 60 cm.

Find the height of the ball when it bounces the 10th time.

• 300

• 6

• 4.5

• 250

You have $729 in the bank on Day 1, $243 on Day 2, and $81 on Day 3. Write the explicit formula that expresses the sequence.

• a_n = 729(1/3)^n-1

• a_n = 729(3)^n-1

• a_n = 1/3(a_n-1)

• a_n = 1/3(729)^n-1

A pendulum that is released to swing freely travels 18 cm on the first swing. On each successive swing, the pendulum travels 80% of the distance of the previous swing. What is the total distance the pendulum swings?

This image shows how a certain bacteria grows in a petri dish. What is the common ratio of this sequence?

• 4

• 3

• 2

• 6

Answer explanation

The number DOUBLES

Determine whether the sequence converges or diverges. If it converges, give the limit.

• Diverges

• Converges to 1

• Converges to 0

Find an explicit rule for the nth term of the sequence

• a_n= 36n-337

• a_n= -201+36(n-1)

• a_n= 37n-338

• a_n= -301+37(n-1)

Find the sum of the arithmetic series using a formula.

• 516, 240

• 516,242

• 116, 242

• 506, 242

Find the first 6 terms of the sequence.

• 13, 19, 25, 31, 37, 43

• 7, 13, 19, 25, 31, 37

• 1, 7, 13, 19, 25, 31

• 7, 12, 17, 22, 27, 32