Problem 19 - College Algebra

Question

The general term of a sequence is given and involves a factorial. Write the first four terms of each sequence. $$a_{n}=\frac{n^{2}}{n !}$$

Step-by-Step Solution

Answer

The first four terms of the sequence are 1, 2, 3, and 2.

Step 1: Substitute n=1 into the general term

First, \(n=1\) is substituted into the equation to get the first term: \(a_{1}=\frac{1^{2}}{1 !} = 1\)

Step 2: Substitute n=2 into the general term

Next, \(n=2\) is substituted into the equation to generate the second term: \(a_{2}=\frac{2^{2}}{2 !} = 2\)

Step 3: Substitute n=3 into the general term

Thirdly, \(n=3\) is substituted into the equation to generate the third term: \(a_{3}=\frac{3^{2}}{3 !} = 3\)

Step 4: Substitute n=4 into the general term

Finally, \(n=4\) is substituted into the equation to generate the fourth term: \(a_{4}=\frac{4^{2}}{4 !} = 2\)