Chapter 12: Q. 12.1 (page 1167)

Find a general term for the sequence whose first five terms are shown $\frac{1}{2}, \frac{1}{4}, \frac{1}{8}, \frac{1}{16}, \frac{1}{32}, \dots$

Short Answer

Expert verified

The general term for the given sequence is $a_{n} = \frac{1}{2^{n}} .$

Step by step solution

Step 1. Given information

$\begin{array}{l} Thegivensequenceis \\ \frac{1}{2}, \frac{1}{4}, \frac{1}{8}, \frac{1}{16}, \frac{1}{32}, \dots \\ Wehavetofindthegeneraltermforthegivensequence. \end{array}$

Step 2. Observing the pattern

$\begin{array}{l} n & 1 & 2 & 3 & 4 & 5 & ... & n \\ Terms & \frac{1}{2} & \frac{1}{4} & \frac{1}{8} & \frac{1}{16} & \frac{1}{32} & ... \\ Pattern & \frac{1}{2^{1}} & \frac{1}{2^{2}} & \frac{1}{2^{3}} & \frac{1}{2^{4}} & \frac{1}{2^{5}} & ... & \frac{1}{2^{n}} \end{array}$

Step 3. Conclusion

We can observe that the numerators are all 1 and the denominators are powers of 2.

Therefore, the general term will be $a_{n} = \frac{1}{2^{n}}$

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.

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.

Find a general term for the sequence whose first five terms are shown $\frac{1}{2}, \frac{1}{4}, \frac{1}{8}, \frac{1}{16}, \frac{1}{32}, \dots$

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

Probability and Statistics

Pure Maths

Calculus

Logic and Functions

Theoretical and Mathematical Physics

Statistics

Study anywhere. Anytime. Across all devices.

Find a general term for the sequence whose first five terms are shown12,14,18,116,132,…

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

Probability and Statistics

Pure Maths

Calculus

Logic and Functions

Theoretical and Mathematical Physics

Statistics

Study anywhere. Anytime. Across all devices.

Find a general term for the sequence whose first five terms are shown $\frac{1}{2}, \frac{1}{4}, \frac{1}{8}, \frac{1}{16}, \frac{1}{32}, \dots$