Sequences and Series Unit Test

Does the infinite geometric series diverge or converge? Explain. 2 + 6 + 18 + 54 + ...

It diverges; it does not have a sum.

What is a possible value for the missing term of the geometric sequence? 39, ___ , 975, ...

-195

What is the 12th term of the sequence 20, 16, 12, ...?

-24

What is the 10th term of the sequence 64, 16, 4, ....?

1/4096

What is the sum of the first 10 terms of the sequence defined by an = 4n - 3?

190

Find the missing term of the arithmetic sequence 22, ___ , 34, ...

28

What is the sum of the geometric series 15 sigma x=0 2(1/4)^x rounded to the nearest whole number?

3

Suppose you drop a tennis ball from a height of 9 feet. After the ball hits the floor, it rebounds to 80% of its previous height. How high will the ball rebound after its third bounce? Round to the nearest tenth.

4.6 feet

What is the sum of the arithmetic series 18 sigma t=1 (3t - 4)?

441

What is the sum of the finite arithmetic series? (-5) + 0 + 5 + 10 + ... + 65

450

Use summation notation to write the series 2.2 + 8.8 + 15.4 +.... for 5 terms Note: In each of these images, the lower limit of the summation notation is either "n = 1" or "n = 0".

5 sigma n=1 (-4.4+6.6n)

A rubber ball dropped on a hard surface takes a sequence of bounces, each one 4/5 as high as the preceding one. If this ball is dropped from a height of 10 feet, what is the total vertical distance it has traveled at the time when it hits the surface for its fifth bounce?

57 29/125 feet

What are the first five terms of the sequence given by the formula an = 5n + 1?

6,11,16,21,26

Write a recursive definition for the sequence 8, 6, 4, 2, ...

a1 = 8; an= an-1 − 2

Write an explicit formula for the sequence -3, 1, 5, 9,...

an = -3 + 4(n - 1)

The table shows the predicted growth of particular bacterium after various numbers of hours. Write an explicit formula for the sequence of the number of bacterium.

an = 24n

Is the sequence arithmetic? If so, identify the common difference. 17, 22, 33, 46, ...

no

Is the sequence geometric? If so, identify the common ratio. 1/4, 3/16, 9/64, 27/256, 81/1024, ...

yes; 3/4