Chapter 12: Q. 321 (page 1222)

In the following exercises, write the first five terms of the sequence whose general term is given.
$a_{n} = \frac{(n + 2)!}{(n + 3)!}$

Short Answer

Expert verified

The first five terms of the sequence $a_{n} = \frac{(n + 2)!}{(n + 3)!}$ is $\frac{1}{4}, \frac{1}{5}, \frac{1}{6}, \frac{1}{7}, \frac{1}{8}$

Step by step solution

Step 1. Given

The general term of the sequence is $a_{n} = \frac{(n + 2)!}{(n + 3)!}$

To find the first five terms of the sequence.

Step 2. Substitute 1,2 in the general form

Substitute the values $1, 2$ in the general form of the sequence,

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

$a_{2} = \frac{((2) + 2)!}{((2) + 3)!} = \frac{4!}{5!} = \frac{1}{5}$

Step 3. Substitute 3,4,5 in the general from.

$a_{3} = \frac{((3) + 2)!}{((3) + 3)!} = \frac{5!}{6!} = \frac{1}{6}$

$a_{4} = \frac{((4) + 2)!}{((4) + 3)!} = \frac{6!}{7!} = \frac{1}{7}$

$a_{5} = \frac{((5) + 2)!}{((5) + 3)!} = \frac{7!}{8!} = \frac{1}{8}$

The five terms of the sequence are $\frac{1}{4}, \frac{1}{5}, \frac{1}{6}, \frac{1}{7}, \frac{1}{8}$

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In the following exercises, write the first five terms of the sequence whose general term is given.
$a_{n} = \frac{(n + 2)!}{(n + 3)!}$

Short Answer

Step by step solution

Step 1. Given

Step 2. Substitute 1,2 in the general form

Step 3. Substitute 3,4,5 in the general from.

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In the following exercises, write the first five terms of the sequence whose general term is given.an=(n+2)!(n+3)!

Short Answer

Step by step solution

Step 1. Given

Step 2. Substitute 1,2 in the general form

Step 3. Substitute 3,4,5 in the general from.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Theoretical and Mathematical Physics

Geometry

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Applied Mathematics

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Decision Maths

Study anywhere. Anytime. Across all devices.

In the following exercises, write the first five terms of the sequence whose general term is given.
$a_{n} = \frac{(n + 2)!}{(n + 3)!}$