Chapter 7: Q. 43 (page 592)

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

Short Answer

Expert verified

The first five terms are $3, \frac{3}{2}, \frac{3}{4}, \frac{3}{8}, \frac{3}{16}$ .

Step by step solution

Step 1. Given information.

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

Step 2. First term.

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

On substituting the given values,

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

For first term, $k = 0,$

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

Step 3. Remaining terms.

Now, when,

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

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

Short Answer

Step by step solution

Step 1. Given information.

Step 2. First term.

Step 3. Remaining terms.

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In Exercises 43–46 give the first five terms for a geometric sequence crk,k=0with the specified values of candr.c=3,r=12.

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 $\{c r^{k}\}, k = 0$ with the specified values of $c a n d r .$
$c = 3, r = \frac{1}{2}$ .