Problem 2 - College Algebra

Question

Write the first four terms of each sequence whose general term is given. $$a_{n}=4 n-1$$

Step-by-Step Solution

Answer

The first four terms of the sequence are 3, 7, 11, 15

Step 1: Compute the first term

Substitute \(n = 1\) in the general term, \(a_{n}=4n - 1\). After simplifying, the 1st term in the sequence, \(a_{1}=4(1)-1=3\)

Step 2: Compute the second term

Substitute \(n = 2\) in the general term, \(a_{n}=4n - 1\). After simplifying, the 2nd term in the sequence, \(a_{2}=4(2)-1=7\)

Step 3: Compute the third term

Substitute \(n = 3\) in the general term, \(a_{n}=4n - 1\). After simplifying, the 3rd term in the sequence, \(a_{3}=4(3)-1=11\)

Step 4: Compute the fourth term

Substitute \(n = 4\) in the general term, \(a_{n}=4n - 1\). After simplifying, the 4th term in the sequence, \(a_{4}=4(4)-1=15\)