Chapter 12: Q. 14 (page 1173)

In the following exercise, write the first five terms of the sequence whose general term is given.
$a_{n} = {(- 1)}^{n} \cdot 3 n$

Short Answer

Expert verified

The first five terms of the sequence whose general term is $a_{n} = {(- 1)}^{n} \cdot 3 n$ are $- 3, 6, - 9, 12, - 15.$

Step by step solution

Step 1. Given information

$\begin{array}{l} Thegeneraltermisgivenas \\ a_{n} = {(- 1)}^{n} \cdot 3 n \\ Wehavetofindthefirstfivetermsofthesequence. \end{array}$

Step 2. Step 2. Calculating the terms

$\begin{array}{l} Wewillsubstitute n = 1, 2, 3, 4 and 5 inordertofindtheterms. \\ Now, \end{array}$

\begin{matrix} n : & 1 & 2 & 3 & 4 & 5 \\ a_{n} : & \begin{array}{l} a_{1} = {(- 1)}^{1} \cdot 3 (1) \\ = - 1 \cdot 3 \\ = - 3 \end{array} & \begin{array}{l} a_{2} = {(- 1)}^{2} \cdot 3 (2) \\ = 1 \cdot 6 \\ = 6 \end{array} & \begin{array}{l} a_{3} = {(- 1)}^{3} \cdot 3 (3) \\ = - 1 \cdot 9 \\ = - 9 \end{array} & \begin{array}{l} a_{4} = {(- 1)}^{4} \cdot 3 (4) \\ = 1 \cdot 12 \\ = 12 \end{array} & \begin{array}{l} a_{5} = {(- 1)}^{5} \cdot 3 (5) \\ = - 1 \cdot 15 \\ = - 15 \end{array} \end{matrix}

Step 3. Conclusion

From the above step, we can conclude that the first five terms of the sequence will be $- 3, 6, - 9, 12, - 15.$

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.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

In the following exercise, write the first five terms of the sequence whose general term is given.
$a_{n} = {(- 1)}^{n} \cdot 3 n$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Step 2. Calculating the terms

Step 3. Conclusion

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Statistics

Applied Mathematics

Theoretical and Mathematical Physics

Calculus

Pure Maths

Study anywhere. Anytime. Across all devices.

In the following exercise, write the first five terms of the sequence whose general term is given.an=−1n⋅3n

Short Answer

Step by step solution

Step 1. Given information

Step 2. Step 2. Calculating the terms

Step 3. Conclusion

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Discrete Mathematics

Statistics

Applied Mathematics

Theoretical and Mathematical Physics

Calculus

Pure Maths

Study anywhere. Anytime. Across all devices.

In the following exercise, write the first five terms of the sequence whose general term is given.
$a_{n} = {(- 1)}^{n} \cdot 3 n$