Q. 243 In the following exercises, writ... [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. 243 (page 1217)

In the following exercises, write the first five terms of the sequence whose general term is given.
$a_{n} = \frac{2 n + 1}{4^{n}}$

Short Answer

Expert verified

The first five terms of the sequence with general term $a_{n} = \frac{2 n + 1}{4^{n}}$ are localid="1645623915255" $\frac{3}{4}, \frac{5}{16}, \frac{7}{64}, \frac{9}{256} and \frac{11}{1024}$ .

Step by step solution

Step 1. Given information.

Write the first five terms of the sequence whose general term is given as

$a_{n} = \frac{2 n + 1}{4^{n}}$ .

Step 2. Calculating the first five terms.

We substitute the values 1, 2, 3, 4, 5 into the formula for the general term.

$\begin{array}{rcl} a_{n} & = & \frac{2 n + 1}{4^{n}} 鈥� 鈥� 鈥� 鈥� 鈥� a_{n} = \frac{2 n + 1}{4^{n}} 鈥� 鈥� 鈥� 鈥� 鈥� a_{n} = \frac{2 n + 1}{4^{n}} 鈥� 鈥� 鈥� 鈥� 鈥� a_{n} = \frac{2 n + 1}{4^{n}} 鈥� 鈥� 鈥� 鈥� 鈥� a_{n} = \frac{2 n + 1}{4^{n}} \\ a_{1} & = & \frac{2 路 1 + 1}{4^{1}} 鈥� 鈥� 鈥� 鈥� a_{2} = \frac{2 路 2 + 1}{4^{2}} 鈥� 鈥� 鈥� 鈥� a_{3} = \frac{2 路 3 + 1}{4^{3}} 鈥� 鈥� 鈥� 鈥� 鈥� a_{4} = \frac{2 路 4 + 1}{4^{4}} 鈥� 鈥� 鈥� 鈥� a_{5} = \frac{2 路 5 + 1}{4^{5}} \\ a_{1} & = & \frac{3}{4} 鈥� 鈥� 鈥� 鈥� 鈥� 鈥� 鈥� 鈥� a_{2} = \frac{5}{16} 鈥� 鈥� 鈥� 鈥� 鈥� 鈥� 鈥� a_{3} = \frac{7}{64} 鈥� 鈥� 鈥� 鈥� 鈥� 鈥� 鈥� a_{4} = \frac{9}{256} 鈥� 鈥� 鈥� 鈥� 鈥� 鈥� 鈥� 鈥� a_{5} = \frac{11}{1024} \end{array}$

The first five terms of the sequence are $\frac{3}{4}, \frac{5}{16}, \frac{7}{64}, \frac{9}{256} and \frac{11}{1024}$ .

Step 3. Conclusion.

Hence, the first five terms of the sequence are $\frac{3}{4}, \frac{5}{16}, \frac{7}{64}, \frac{9}{256} and \frac{11}{1024}$ .

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91影视

In the following exercises, write the first five terms of the sequence whose general term is given.
$a_{n} = \frac{2 n + 1}{4^{n}}$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Calculating the first five terms.

Step 3. Conclusion.

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91影视

In the following exercises, write the first five terms of the sequence whose general term is given.an=2n+14n

Short Answer

Step by step solution

Step 1. Given information.

Step 2. Calculating the first five terms.

Step 3. Conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Pure Maths

Logic and Functions

Discrete Mathematics

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Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

In the following exercises, write the first five terms of the sequence whose general term is given.
$a_{n} = \frac{2 n + 1}{4^{n}}$