Chapter 14, Sequences and Series Video Solutions, Precalculus with Trigonometry: Concepts and Applications

Problem 1

The infinite set of numbers $5,7,9,11, \ldots$ is an arithmetic sequence. It progresses by adding 2 to one term to get the next term. What does the tenth term equal? How many 2 s would you have to add to the first term, $5,$ to get the tenth term? How could you get the tenth term quickly? Find the 100 th term quickly.

Nolwazi Dube

Numerade Educator

01:28

Problem 2

Enter the first ten terms of the sequence in Problem 1 in a list in your grapher, and enter the term numbers $1,2,3,4, \ldots, 10$ in another list. Make a point plot of term value as a function of term number. Sketch.

Nolwazi Dube

Numerade Educator

01:29

Problem 3

What kind of continuous function contains all the points in the plot of Problem $2 ?$

Nolwazi Dube

Numerade Educator

01:20

Problem 4

The infinite $\operatorname{sum} 5+7+9+11+\cdots$ is an arithmetic series. Because the series has an infinite number of terms, you cannot add them all. But you can add part of the terms. Find the tenth partial sum by adding the first ten terms.

Nolwazi Dube

Numerade Educator

01:20

Problem 5

Find the average of the first and tenth term in the partial sum of Problem 4. Multiply this number by $10 .$ What do you notice about the answer? Use the pattern you observe to find the 100 th partial sum of the series. Show how you did it.

Zach Steedman

Numerade Educator

01:19

Problem 6

Calculate the first ten partial sums of the series in Problem 4 and enter them in a third data list. Make a point plot of partial sum as a function of number of terms, using the term numbers in one of the data lists from Problem $2 .$ Sketch the result.

Ankit Gupta

Numerade Educator

01:29

Problem 7

Run regressions to find out which kind of continuous function exactly fits the partial sums in Problem $6 .$ Write its particular equation. Use the result to find quickly the 100th partial sum of the series.

Varsha Aggarwal

Numerade Educator

02:45

Problem 8

The infinite set of numbers $6,12,24,48, \ldots$ is a geometric sequence. How do the terms progress from one to the next? Find the tenth
term of the sequence.

Nolwazi Dube

Numerade Educator

01:17

Problem 9

The infinite sum $6+12+24+48+\ldots$ is a geometric series. Find the tenth partial sum of the series.

Nolwazi Dube

Numerade Educator

03:16

Problem 10

What did you learn as a result of doing this problem set that you did not know before?

Jocelyn Thammavong

Numerade Educator