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Chapter 10: Problem 7

Write the first five terms of the sequence. $$ a_{n}=\frac{3^{n}}{n !} $$

Short Answer

Expert verified
The first five terms of the sequence are 3, 4.5, 4.5, 6.75, and 20.25.

Step by step solution

01

Identify the First Term

To find the first term of the sequence, substitute \( n \) with 1 in the given function \( a_{n}=\frac{3^{n}}{n !} \). So, \( a_{1}=\frac{3^{1}}{1 !} \) which simplifies to 3.
02

Identify the Second Term

For the second term, substitute \( n \) with 2 in the given function. So, \( a_{2}=\frac{3^{2}}{2 !} \) which simplifies to 4.5.
03

Identify the Third Term

For the third term, substitute \( n \) with 3 in the given function. So, \( a_{3}=\frac{3^{3}}{3 !} \) which simplifies to 4.5.
04

Identify the Fourth Term

For the fourth term, substitute \( n \) with 4 in the given function. So, \( a_{4}=\frac{3^{4}}{4 !} \) which simplifies to 6.75.
05

Identify the Fifth Term

For the fifth term, substitute \( n \) with 5 in the given function. So, \( a_{5}=\frac{3^{5}}{5 !} \) which simplifies to 20.25.

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