Chapter 12: Q 149. (page 1198)

In the following exercises, find the indicated term of a sequence where the first term and the common ratio is given.
Find $a_{10}$ given $a_{1} = 100, 000$ and $r = 0.1$

Short Answer

Expert verified

The value of $a_{10}$ is $0.0001$ .

Step by step solution

Step 1. Write the given information and use the formula of general term

The given information is:

$a_{1} = 100, 000$ and $r = 0.1$

The general term of a geometric sequence with the first term $a_{1}$ and the common ratio $r$ is:

$a_{n} = a_{1} r^{n - 1}$

Step 2. Substitute the given values into the formula

$a_{1} = 100, 000, r = 0.1$ and $n = 10$

localid="1645332117797" $a_{10} = (100, 000) {(0.1)}^{10 - 1} = (100, 000) {(0.1)}^{9} = (100, 000) (0.000000001) = 0.0001$

$a_{10} = 0.0001$

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In the following exercises, find the indicated term of a sequence where the first term and the common ratio is given.
Find $a_{10}$ given $a_{1} = 100, 000$ and $r = 0.1$

Short Answer

Step by step solution

Step 1. Write the given information and use the formula of general term

Step 2. Substitute the given values into the formula

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In the following exercises, find the indicated term of a sequence where the first term and the common ratio is given.Finda10givena1=100,000andr=0.1

Short Answer

Step by step solution

Step 1. Write the given information and use the formula of general term

Step 2. Substitute the given values into the formula

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Applied Mathematics

Probability and Statistics

Discrete Mathematics

Calculus

Decision Maths

Logic and Functions

Study anywhere. Anytime. Across all devices.

In the following exercises, find the indicated term of a sequence where the first term and the common ratio is given.
Find $a_{10}$ given $a_{1} = 100, 000$ and $r = 0.1$