How do you simplify an expression like: aₙ = 5 + (n-1)1

To simplify the expression \( a_n = 5 + (n-1)1 \), follow these steps:

1. **Distribute the 1**: Since multiplying by 1 does not change the value of any expression, you can directly simplify \( (n-1)1 \) to \( n-1 \).

   \[
   a_n = 5 + (n-1)
   \]

2. **Combine like terms**: Now, add the constant terms together.

   \[
   a_n = 5 + n - 1
   \]

   \[
   a_n = n + 4
   \]

So, the simplified expression is \( a_n = n + 4 \).

Would you like more details or have any questions? Here are five related questions to consider:

1. How would you simplify an expression involving other constants and variables?
2. What happens if the coefficient of \( n \) is something other than 1?
3. How does this simplification apply in the context of sequences?
4. What is the significance of combining like terms in algebra?
5. Can you provide an example where you distribute a different number, like 2 or 3, instead of 1?

**Tip:** Always look for opportunities to combine like terms and simplify expressions. It helps in reducing the complexity of calculations and makes it easier to identify patterns.

Learn how to simplify the sequence expression aₙ = 5 + (n-1) step-by-step with detailed explanations. This problem involves algebraic manipulation of arithmetic sequences, focusing on combining like terms and simplifying expressions. Suitable for high school students.

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