Chapter 12: Q 30. (page 809)

In Problems 29–36, the given pattern continues. Write down the nth term of a sequence $\{a_{n}\}$ suggested by the pattern.
role="math" localid="1646738671855" $\frac{1}{1 \cdot 2}, \frac{1}{2 \cdot 3}, \frac{1}{3 \cdot 4}, \frac{1}{4 \cdot 5}, . . .$

Short Answer

Expert verified

The nth term of the sequence is $a_{n} = \frac{1}{n (n + 1)}$

Step by step solution

Step 1. Write the given information.

The given sequence is $\frac{1}{1 \cdot 2}, \frac{1}{2 \cdot 3}, \frac{1}{3 \cdot 4}, \frac{1}{4 \cdot 5}, . . .$

Step 2. Determine the pattern of the sequence and write down the nth term.

$a_{1} = \frac{1}{1 \cdot 2}, a_{2} = \frac{1}{2 \cdot 3}, a_{3} = \frac{1}{3 \cdot 4}$

The pattern of the sequence is:

$a_{1} = \frac{1}{1 \cdot 2} = \frac{1}{1 (1 + 1)} a_{2} = \frac{1}{2 \cdot 3} = \frac{1}{2 (2 + 1)} a_{3} = \frac{1}{3 \cdot 4} = \frac{1}{3 (3 + 1)} a_{n} = \frac{1}{n (n + 1)}$

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In Problems 29–36, the given pattern continues. Write down the nth term of a sequence $\{a_{n}\}$ suggested by the pattern.
role="math" localid="1646738671855" $\frac{1}{1 \cdot 2}, \frac{1}{2 \cdot 3}, \frac{1}{3 \cdot 4}, \frac{1}{4 \cdot 5}, . . .$

Short Answer

Step by step solution

Step 1. Write the given information.

Step 2. Determine the pattern of the sequence and write down the nth term.

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In Problems 29–36, the given pattern continues. Write down the nth term of a sequence ansuggested by the pattern.role="math" localid="1646738671855" 11·2,12·3,13·4,14·5,...

Short Answer

Step by step solution

Step 1. Write the given information.

Step 2. Determine the pattern of the sequence and write down the nth term.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Calculus

Probability and Statistics

Mechanics Maths

Theoretical and Mathematical Physics

Geometry

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

In Problems 29–36, the given pattern continues. Write down the nth term of a sequence $\{a_{n}\}$ suggested by the pattern.
role="math" localid="1646738671855" $\frac{1}{1 \cdot 2}, \frac{1}{2 \cdot 3}, \frac{1}{3 \cdot 4}, \frac{1}{4 \cdot 5}, . . .$