Chapter 7: Q. 46 (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 $c a n d r .$
$c = - 1, r = - \frac{1}{2}$

Short Answer

Expert verified

The first five terms are $- 1, \frac{1}{2}, - \frac{1}{4}, \frac{1}{8}, - \frac{1}{16}$ .

Step by step solution

Step 1. Given information.

The given data is $c = - 1, r = - \frac{1}{2} .$

Step 2. First term.

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

Substituting the given values,

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

For the first term $k = 0,$

Therefore,

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

Step 3. Remaining terms.

Substituting,

$k = 1, a_{1} = (- 1) {(- \frac{1}{2})}^{1} = \frac{1}{2} k = 2 a_{2} = (- 1) {(- \frac{1}{2})}^{2} = - \frac{1}{4} k = 3, a_{3} = (- 1) {(- \frac{1}{2})}^{3} = \frac{1}{8} k = 4 a_{4} = (- 1) {(- \frac{1}{2})}^{4} = - \frac{1}{16}$

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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 $c a n d r .$
$c = - 1, r = - \frac{1}{2}$

Short Answer

Step by step solution

Step 1. Given information.

Step 2. First term.

Step 3. Remaining terms.

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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

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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 $c a n d r .$
$c = - 1, r = - \frac{1}{2}$