91Ó°ÊÓ

In general, sequences are ordered sets of numbers that follow a specific pattern. When dealing with algebraic sequences, we see sequences formed based on algebraic expressions. For example, the sequence given in the problem is defined by the algebraic formula: \[ a_{n} = \frac{n+2}{n} \].
Each term in the sequence corresponds to a unique value of \(n\) substituted into this formula.
Understanding algebraic sequences is fundamental in algebra because they help us recognize patterns and relationships between numbers.

To solve problems involving sequences, it's essential to understand how to calculate individual terms. Each term in an algebraic sequence can be calculated by substituting the values of the position \(n\) into the sequence formula. Let's break it down further:

• **First Term:** Substitute \(n = 1\) into the formula \(a_{n} = \frac{n + 2}{n}\):\( a_{1} = \frac{1+2}{1} = 3 \)
• **Second Term:** Substitute \(n = 2\): \( a_{2} = \frac{2+2}{2} = 2 \)
• **Third Term:** Substitute \(n = 3\): \( a_{3} = \frac{3+2}{3} = \frac{5}{3} \)
• **Fourth Term:** Substitute \(n = 4\): \( a_{4} = \frac{4+2}{4} = \frac{3}{2} \)
• **Fifth Term:** Substitute \(n = 5\): \( a_{5} = \frac{5+2}{5} = \frac{7}{5} \)

This procedure ensures that we follow the ordered steps and correctly find each term.

Breaking down the process in a structured way helps in understanding and solving the problem. Here are the five steps to find the first five terms of the sequence:
First, determine the formula given: \( a_{n} = \frac{n+2}{n} \).

**Step 1: Find the first term**
Substitute \(n = 1\) into the equation: \[ a_{1} = \frac{1+2}{1} = \frac{3}{1} = 3 \]

**Step 2: Find the second term**
Substitute \(n = 2\): \[ a_{2} = \frac{2+2}{2} = \frac{4}{2} = 2 \]

**Step 3: Find the third term**
Substitute \(n = 3\): \[ a_{3} = \frac{3+2}{3} = \frac{5}{3} \]

**Step 4: Find the fourth term**
Substitute \(n = 4\): \[ a_{4} = \frac{4+2}{4} = \frac{6}{4} = \frac{3}{2} \]

**Step 5: Find the fifth term**
Substitute \(n = 5\): \[ a_{5} = \frac{5+2}{5} = \frac{7}{5} \]

Following these steps allows any student to methodically approach and break down the sequence problem.
Consistent practice with these steps will cultivate a deeper understanding and proficiency in working with algebraic sequences.