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" $\begin{array}{l} Weknow \\ If n isapositiveinteger,then \\ \Rightarrow n! = n (n - 1) (n - 2) \dots \\ Now, \\ \begin{matrix} n = 1 & n = 2 & n = 3 & n = 4 & n = 5 \\ \begin{array}{l} \Rightarrow a_{1} = \frac{3}{1!} \\ = \frac{3}{1} \\ = 3 \end{array} & \begin{array}{l} \Rightarrow a_{2} = \frac{3}{2!} \\ = \frac{3}{2 \cdot 1} \\ = \frac{3}{2} \end{array} & \begin{array}{l} \Rightarrow a_{3} = \frac{3}{3!} \\ = \frac{3}{3 \cdot 2 \cdot 1} \\ = \frac{1}{2} \end{array} & \begin{array}{l} \Rightarrow a_{4} = \frac{3}{4!} \\ = \frac{3}{4 \cdot 3 \cdot 2 \cdot 1} \\ = \frac{3}{8} \end{array} & \begin{array}{l} \Rightarrow a_{5} = \frac{3}{5!} \\ = \frac{3}{5 \cdot 4 \cdot 3 \cdot 2 \cdot 1} \\ = \frac{1}{40} \end{array} \end{matrix} \end{array}$

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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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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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

Decision Maths

Logic and Functions

Geometry

Statistics

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Applied Mathematics

Study anywhere. Anytime. Across all devices.

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