Chapter 7: Q. 44 (page 592)

In Exercises 43–46 give the first five terms for a geometric sequence ${\{c r^{k}\}}_{k = 0}^{\infty}$ with the specified values of $c a n d r .$
$c = - 2, r = - \frac{1}{3}$

Short Answer

Expert verified

The five terms are $- 2, \frac{2}{3}, - \frac{2}{9}, \frac{2}{27}, - \frac{2}{81} .$

Step by step solution

Step 1. Given information.

The given values are $c = - 2, r = - \frac{1}{3} .$

Step 2. First term.

The general sequence is $a_{k} = c r^{k} .$

On substituting the given values,

$a_{k} = (- 2) {(- \frac{1}{3})}^{k}$

For first term,

$k = 0, a_{0} = (- 2) {(- \frac{1}{3})}^{0} = - 2$

Step 3. Remaining terms.

Now, when,

$k = 1, a_{1} = (- 2) {(- \frac{1}{3})}^{1} = \frac{2}{3} k = 2, a_{2} = (- 2) {(- \frac{1}{3})}^{2} = - \frac{2}{9} k = 3, a_{3} = (- 2) {(- \frac{1}{3})}^{3} = \frac{2}{27} k = 4, a_{4} = (- 2) {(- \frac{1}{3})}^{4} = - \frac{2}{81}$

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In Exercises 43–46 give the first five terms for a geometric sequence ${\{c r^{k}\}}_{k = 0}^{\infty}$ with the specified values of $c a n d r .$
$c = - 2, r = - \frac{1}{3}$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. First term.

Step 3. Remaining terms.

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In Exercises 43–46 give the first five terms for a geometric sequence crkk=0∞with the specified values of candr.c=-2,r=-13

Short Answer

Step by step solution

Step 1. Given information.

Step 2. First term.

Step 3. Remaining terms.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Statistics

Mechanics Maths

Decision Maths

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Theoretical and Mathematical Physics

Study anywhere. Anytime. Across all devices.

In Exercises 43–46 give the first five terms for a geometric sequence ${\{c r^{k}\}}_{k = 0}^{\infty}$ with the specified values of $c a n d r .$
$c = - 2, r = - \frac{1}{3}$