Q. 34 In the following exercise, find ... [FREE SOLUTION]

91影视

Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 12: Q. 34 (page 1173)

In the following exercise, find a general term for the sequence whose first five terms are shown.
$- 2, - \frac{3}{2}, - \frac{4}{3}, - \frac{5}{4}, - \frac{6}{5}, 鈥�$

Short Answer

Expert verified

The general term for the sequence whose first five terms are $- 2, - \frac{3}{2}, - \frac{4}{3}, - \frac{5}{4}, - \frac{6}{5}, 鈥�$ is $a_{n} = 鈭� \frac{n + 1}{n} .$

Step by step solution

Step 1. Given information

$\begin{array}{l} Thefirstfivetermsofthesequenceare \\ 鈭� 2, 鈭� \frac{3}{2}, 鈭� \frac{4}{3}, 鈭� \frac{5}{4}, 鈭� \frac{6}{5}, 鈥� \\ Wehavetofindthegeneraltermforthesequence. \end{array}$

Step 2. Observing the pattern

Now,

$\begin{matrix} n : & 1 & 2 & 3 & 4 & 5 & ... & n \\ Terms: & 鈭� 2 & 鈭� \frac{3}{2} & 鈭� \frac{4}{3} & 鈭� \frac{5}{4} & 鈭� \frac{6}{5} & ... \\ Pattern & 鈭� \frac{1 + 1}{1} & 鈭� \frac{2 + 1}{2} & 鈭� \frac{3 + 1}{3} & 鈭� \frac{4 + 1}{4} & 鈭� \frac{5 + 1}{5} & ... & 鈭� \frac{n + 1}{n} \end{matrix}$

Step 3. Conclusion

From the above table, we can observe that the general terms will be $a_{n} = 鈭� \frac{n + 1}{n} .$

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

91影视

In the following exercise, find a general term for the sequence whose first five terms are shown.
$- 2, - \frac{3}{2}, - \frac{4}{3}, - \frac{5}{4}, - \frac{6}{5}, 鈥�$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Observing the pattern

Step 3. Conclusion

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Applied Mathematics

Calculus

Theoretical and Mathematical Physics

Probability and Statistics

Mechanics Maths

Study anywhere. Anytime. Across all devices.

91影视

In the following exercise, find a general term for the sequence whose first five terms are shown. -2,-32,-43,-54,-65,鈥�

Short Answer

Step by step solution

Step 1. Given information

Step 2. Observing the pattern

Step 3. Conclusion

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Geometry

Applied Mathematics

Calculus

Theoretical and Mathematical Physics

Probability and Statistics

Mechanics Maths

Study anywhere. Anytime. Across all devices.

In the following exercise, find a general term for the sequence whose first five terms are shown.
$- 2, - \frac{3}{2}, - \frac{4}{3}, - \frac{5}{4}, - \frac{6}{5}, 鈥�$