Q. 12.14 Write the first five terms of th... [FREE SOLUTION]

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Intermediate Algebra

OPENSTAX

$Math Studyset 91影视 Explanations$ Math

OER 2017 Edition 路 1346 pages

ISBN: 9780998625720

Chapter 12: Q. 12.14 (page 1168)

Write the first five terms of the sequence whose general term is $a_{n} = \frac{3}{n!}$

Short Answer

Expert verified

The first five terms of the sequence are $3, \frac{3}{2}, \frac{1}{2}, \frac{3}{8} and \frac{1}{40} .$

Step by step solution

Step 1. Given information

$\begin{array}{l} Thegivengeneraltermis \\ a_{n} = \frac{3}{n!} \\ Wehavetofindthefirstfivetermofthesequence. \end{array}$

Step 2. Calculating the first five terms

We substitute the values 1, 2, 3, 4, 5 into the formula $a_{n} = \frac{3}{n!}$

localid="1645105874281" $\begin{array}{l} Weknow \\ If n isapositiveinteger,then \\ 鈬� n! = n (n 鈭� 1) (n 鈭� 2) 鈥� \\ Now, \\ \begin{matrix} n = 1 & n = 2 & n = 3 & n = 4 & n = 5 \\ \begin{array}{l} 鈬� a_{1} = \frac{3}{1!} \\ = \frac{3}{1} \\ = 3 \end{array} & \begin{array}{l} 鈬� a_{2} = \frac{3}{2!} \\ = \frac{3}{2 鈰� 1} \\ = \frac{3}{2} \end{array} & \begin{array}{l} 鈬� a_{3} = \frac{3}{3!} \\ = \frac{3}{3 鈰� 2 鈰� 1} \\ = \frac{1}{2} \end{array} & \begin{array}{l} 鈬� a_{4} = \frac{3}{4!} \\ = \frac{3}{4 鈰� 3 鈰� 2 鈰� 1} \\ = \frac{3}{8} \end{array} & \begin{array}{l} 鈬� a_{5} = \frac{3}{5!} \\ = \frac{3}{5 鈰� 4 鈰� 3 鈰� 2 鈰� 1} \\ = \frac{1}{40} \end{array} \end{matrix} \end{array}$

Therefore, the first five terms of the sequence will be $3, \frac{3}{2}, \frac{1}{2}, \frac{3}{8} and \frac{1}{40} .$

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91影视

Write the first five terms of the sequence whose general term is $a_{n} = \frac{3}{n!}$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Calculating the first five terms

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91影视

Write the first five terms of the sequence whose general term isan=3n!

Short Answer

Step by step solution

Step 1. Given information

Step 2. Calculating the first five terms

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

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Write the first five terms of the sequence whose general term is $a_{n} = \frac{3}{n!}$